|
MOOCHO
Version of the Day
|
|
Below is the output file MoochoJournal.out from the program ExampleNLPBanded.exe using the command-line arguments
--echo-command-line --nD=3000 --bw=10 --diag-scal=1e+3 --nI=5 --xIl=1e-5 --xo=0.1
given the Moocho.opt options file shown here.
Here is the other types of output that is associated with this run:
Output file MoochoJournal.out:
********************************************************************
*** Algorithm iteration detailed journal output ***
*** ***
*** Below, detailed information about the SQP algorithm is given ***
*** while it is running. The amount of information that is ***
*** produced can be specified using the option ***
*** NLPSolverClientInterface::journal_output_level (the default ***
*** is PRINT_NOTHING and produces no output ***
********************************************************************
*** Echoing input options ...
begin_options
options_group DecompositionSystemStateStepBuilderStd {
null_space_matrix = EXPLICIT;
range_space_matrix = ORTHOGONAL;
}
options_group NLPAlgoConfigMamaJama {
line_search_method = FILTER;
quasi_newton = BFGS;
}
options_group NLPSolverClientInterface {
calc_conditioning = true;
calc_matrix_info_null_space_only = true;
calc_matrix_norms = true;
feas_tol = 1e-7;
journal_output_level = PRINT_ALGORITHM_STEPS;
journal_print_digits = 10;
max_iter = 20;
max_run_time = 2.0;
null_space_journal_output_level = PRINT_ITERATION_QUANTITIES;
opt_tol = 1e-2;
}
end_options
*** Setting up to run MOOCHO on the NLP using a configuration object of type 'MoochoPack::NLPAlgoConfigMamaJama' ...
*****************************
*** MoochoSolver::solve() ***
*****************************
test_nlp = true: Testing the NLP! ...
Testing the supported NLPFirstOrder interface ...
*********************************
*** test_nlp_first_order(...) ***
*********************************
Testing the vector spaces ...
Testing nlp->space_x() ...
nlp->space_x() checks out!
Testing nlp->space_c() ...
nlp->space_c() checks out!
**************************************
*** NLPTester::test_interface(...) ***
**************************************
nlp->force_xinit_in_bounds(true)
nlp->initialize(true)
*** Dimensions of the NLP ...
nlp->n() = 3005
nlp->m() = 3000
*** Validate the dimensions of the vector spaces ...
check: nlp->space_x()->dim() = 3005 == nlp->n() = 3005: true
check: nlp->space_c()->dim() = 3000 == nlp->m() = 3000: true
*** Validate that the initial starting point is in bounds ...
||nlp->xinit()||inf = 1.00000000e-01
check: xl <= x <= xu : true
xinit is in bounds with { max |u| | xl <= x + u <= xu } -> 1.00000000e+50
check: num_bounded(nlp->xl(),nlp->xu()) = 5 == nlp->num_bounded_x() = 5: true
Getting the initial estimates for the Lagrange mutipliers ...
||lambda||inf = 0.00000000e+00
||nu||inf = 0.00000000e+00
nu.nz() = 0
*** Evaluate the point xo ...
||xo||inf = 1.00000000e-01
f(xo) = 1.50250000e+01
||c(xo)||inf = 1.19973085e+02
*** Report this point to the NLP as suboptimal ...
*** Print the number of evaluations ...
nlp->num_f_evals() = 1
nlp->num_c_evals() = 1
Calling nlp->calc_Gc(...) at nlp->xinit() ...
Calling nlp->calc_Gf(...) at nlp->xinit() ...
Comparing directional products Gf'*y and/or Gc'*y with finite difference values FDGf'*y and/or FDGc'*y for random y's ...
****
**** Random directional vector 1 ( ||y||_1 / n = 5.02523278e-01 )
***
rel_err(Gf'*y,FDGf'*y) = rel_err(-3.72976994e+00,-3.72976994e+00) = 1.20314339e-13
rel_err(sum(Gc'*y),sum(FDGc'*y)) = rel_err(3.34447607e+03,3.34447607e+03) = 3.22588066e-13
Congradulations! All of the computed errors were within the specified error tolerance!
Successful end of testing of the nlp
************************************
*** MoochoSolver::solve_nlp() ***
************************************
*** Starting iterations ...
(0) 1: "EvalNewPoint"
x is not updated for any k so set x_k = nlp.xinit() ...
||x_k||inf = 1.0000000000e-01
Updating the decomposition ...
DecompositionSystemVarReductPerm object currently does not have a basis so we must select one ...
The NLP will attempt to select a basis (k = 0)...
****************************************************************
*** DecompositionSystemVarReductImp::get_basis_matrices(...) ***
****************************************************************
Must allocate a new matrix object for D = -inv(C)*N since one has not been allocated yet ...
Allocated a new explicit matrix object for D = -inv(C)*N of type 'AbstractLinAlgPack::MultiVectorMutableDense' ...
Must allocate a new basis matrix object for C since one has not been allocated yet ...
Allocated a new basis matrix object C of type 'AbstractLinAlgPack::MatrixOpNonsingAggr' ...
End DecompositionSystemVarReductImp::get_basis_matrices(...)
Using a direct sparse solver to set a new basis ...
Using LAPACK xGETRF to analyze and factor a new matrix ...
***********************************************************
*** DecompositionSystemVarReductImp::update_decomp(...) ***
************************************************************
Warning!!! mat_rel != MATRICES_INDEP_IMPS; The decompsition matrix objects may not be independent of each other!
End DecompositionSystemVarReductImp::update_decomp(...)
Printing the updated iteration quantities ...
f_k = 1.5025000000e+01
||Gf_k||inf = 1.0000000000e-01
||Gf_k(var_dep)_k||inf = 1.0000000000e-01
||Gf_k(var_indep)_k||inf = 1.0000000000e-01
||c_k||inf = 1.1997308452e+02
Gf(var_indep)_k =
5
0.1:1 0.1:2 0.1:3 0.1:4 0.1:5
(0) 2: "QuasiNormalStep"
||py|| = 4.7998936932e-03
||Ypy||2 = 1.1999603325e+00
(0) 2.1: "CheckDecompositionFromPy"
beta = ||py||/||c|| = 4.0008087749e-05
num_basis_k was updated so the basis changed so we will skip this check
reset min ||py||/||c|| to current value + 1
(0) 2.2: "CheckDecompositionFromRPy"
beta = ||R*py_k + c_k(decomp)||inf / (||c_k(decomp)||inf + small_number)
= 1.3784529074e-11 / (1.1997308452e+02 + 2.2250738585e-308)
= 1.1489684648e-13
num_basis_k was updated so the basis changed so we will skip this check
reset min ||R*py+c||/||c|| to current value + epsilon(2.2204460493e-16)
(0) 3: "ReducedGradient"
||rGf||inf = 1.0809594644e+01
rGf_k =
5
-10.8086:1 -10.8091:2 -10.8091:3 -10.8091:4 -10.8096:5
(0) 4.-1: "CheckSkipBFGSUpdate"
(0) 4: "ReducedHessian"
Initializing rHL = eye(n-r) (k = 0)...
||rHL_k||inf = 1.0000000000e+00
cond_inf(rHL_k) = 1.0000000000e+00
rHL_k =
Unfactored symmetric matrix stored as lower triangle (ignore upper nonzeros):
5 5
1:1:1 0:1:2 1:1:3 0:1:4 0:1:5
0:2:1 1:2:2 0:2:3 1:2:4 0:2:5
0:3:1 0:3:2 1:3:3 0:3:4 1:3:5
0:4:1 0:4:2 0:4:3 1:4:4 0:4:5
0:5:1 0:5:2 0:5:3 0:5:4 1:5:5
Matrix scaling M = scale*U'*U, scale = 1
Upper cholesky factor U (ignore lower nonzeros):
5 5
1:1:1 0:1:2 0:1:3 0:1:4 0:1:5
0:2:1 1:2:2 0:2:3 0:2:4 0:2:5
1:3:1 0:3:2 1:3:3 0:3:4 0:3:5
0:4:1 1:4:2 0:4:3 1:4:4 0:4:5
0:5:1 0:5:2 1:5:3 0:5:4 1:5:5
(0) 5.-1: "SetDBoundsStd"
(0) 5: "TangentialStep"
qp_grad_k =
5
-10.8086:1 -10.8091:2 -10.8091:3 -10.8091:4 -10.8096:5
Determine if we can use simple bounds on pz ...
m = 3000
dynamic_cast<const MatrixIdentConcat*>(&Z_k) = 0xe2c76b0
||Ypy_k(var_indep)||inf = 5.2360290589e-01
Using simple bounds on pz ...
There are no finite bounds on dependent variables. There will be no extra inequality constraints added on D*pz ...
Calling QPKWIK to solve QP problem ...
||pz_k||inf = 1.0809594644e+01
nu_k.nz() = 0
max(|nu_k(i)|) = 0.0000000000e+00
||Zpz_k||2 = 1.1032346914e+02
pz_k =
5
10.8086:1 10.8091:2 10.8091:3 10.8091:4 10.8096:5
nu_k(var_indep) =
5
0:1 0:2 0:3 0:4 0:5
Zpz(var_indep)_k =
5
10.8086:1 10.8091:2 10.8091:3 10.8091:4 10.8096:5
(0) 6: "CalcDFromYPYZPZ"
(Ypy_k'*Zpz_k)/(||Ypy_k||2 * ||Zpz_k||2 + eps)
= (-1.3207213101e-12)/(1.1999603325e+00 * 1.1032346914e+02 + 2.2250738585e-308)
= -9.9764581665e-15
||d_k||inf = 1.0285991738e+01
(0) 7: "CalcReducedGradLagrangian"
||rGL_k||inf = 1.0809594644e+01
rGL_k =
5
-10.8086:1 -10.8091:2 -10.8091:3 -10.8091:4 -10.8096:5
(0) 8: "CheckConvergence"
scale_opt_factor = 1.0000000000e+00 (scale_opt_error_by = SCALE_BY_ONE)
scale_feas_factor = 1.0000000000e+00 (scale_feas_error_by = SCALE_BY_ONE)
scale_comp_factor = 1.0000000000e+00 (scale_comp_error_by = SCALE_BY_ONE)
opt_scale_factor = 1.1000000000e+00 (scale_opt_error_by_Gf = true)
opt_kkt_err_k = 9.8269042215e+00 > opt_tol = 1.0000000000e-02
feas_kkt_err_k = 1.1997308452e+02 > feas_tol = 1.0000000000e-07
comp_kkt_err_k = -0.0000000000e+00 < comp_tol = 1.0000000000e-06
step_err = 9.3509015798e+00 > step_tol = 1.0000000000e-02
Have not found the solution yet, have to keep going (k = 0) :-(
(0) 9.-1: "LineSearchFullStep"
f_k = 1.5025000000e+01
||c_k||inf = 1.1997308452e+02
alpha_k = 1.0000000000e+00
||x_kp1||inf = 1.0385991738e+01
f_kp1 = 5.5154949366e+03
||c_kp1||inf = 2.4039402261e+05
(0) 9: "LineSearch"
theta_k = ||c_k||1/c_k.dim() = 1.1792252057e+02
f_min==F_MIN_UNBOUNDED: Setting gamma_f_used = gamma_f = 1.0000000000e-05.
Beginning Filter line search method.
Current Filter
-----------------------------------------------------
| f_with_boundary | theta_with_boundary |
-----------------------------------------------------
Filter is empty.
Iteration Status
----------------------------------------------------------------------------------------------------------
| alpha_k | f_kp1 | theta_kp1 | pt. status | comment |
----------------------------------------------------------------------------------------------------------
|1.0000000000e+00 5.5154949366e+03 2.3625283841e+05 failed Fraction Reduction (! Switch Cond )|
|5.0000000000e-01 1.2436714997e+03 3.3614573874e+04 failed Fraction Reduction (! Switch Cond )|
|2.5000000000e-01 2.4895113274e+02 5.1562325845e+03 failed Fraction Reduction (! Switch Cond )|
|1.2500000000e-01 3.6888787086e+01 8.1127274965e+02 failed Fraction Reduction (! Switch Cond )|
|6.2500000000e-02 2.1820737219e+00 6.8472167804e+01 accepted Fraction Reduction (! Switch Cond )|
Point was accepted - augmenting the filter ...
Augmenting the filter with the point:
f_with_boundary = f_kp1 - gamma_f_used*theta_kp1 = 2.1820737219e+00 - 1.0000000000e-05*6.8472167804e+01 = 2.1813890002e+00
theta_with_boundary = (1-gamma_theta)*theta_kp1 = (1-1.0000000000e-05)*6.8472167804e+01 = 6.8471483083e+01
(1) 1: "EvalNewPoint"
||x_k||inf = 7.4287448361e-01
||x(var_dep)_k||inf = 2.3136269747e-02
||x(var_indep)_k||inf = 7.4287448361e-01
x(var_indep)_k =
5
0.742812:1 0.742843:2 0.742843:3 0.742843:4 0.742874:5
Updating the decomposition ...
Updating the range/null decompostion matrices ...
***********************************************************
*** DecompositionSystemVarReductImp::update_decomp(...) ***
************************************************************
Warning!!! mat_rel != MATRICES_INDEP_IMPS; The decompsition matrix objects may not be independent of each other!
****************************************************************
*** DecompositionSystemVarReductImp::get_basis_matrices(...) ***
****************************************************************
Allocated a new explicit matrix object for D = -inv(C)*N of type 'AbstractLinAlgPack::MultiVectorMutableDense' ...
End DecompositionSystemVarReductImp::get_basis_matrices(...)
Updating the basis matrix C and other matices using the BasisSystem object ...
Using a direct sparse solver to update basis ...
Using LAPACK xGETRF to refactor the basis matrix ...
End DecompositionSystemVarReductImp::update_decomp(...)
Printing the updated iteration quantities ...
f_k = 2.1820737219e+00
||Gf_k||inf = 7.4287448361e-01
||Gf_k(var_dep)_k||inf = 2.3136269747e-02
||Gf_k(var_indep)_k||inf = 7.4287448361e-01
||c_k||inf = 6.9682547090e+01
Gf(var_indep)_k =
5
0.742812:1 0.742843:2 0.742843:3 0.742843:4 0.742874:5
(1) 2: "QuasiNormalStep"
||py|| = 1.6259405998e-02
||Ypy||2 = 1.0621477516e+00
(1) 2.1: "CheckDecompositionFromPy"
beta = ||py||/||c|| = 2.3333541435e-04
(1) 2.2: "CheckDecompositionFromRPy"
beta = ||R*py_k + c_k(decomp)||inf / (||c_k(decomp)||inf + small_number)
= 6.8212102633e-13 / (6.9682547090e+01 + 2.2250738585e-308)
= 9.7889795195e-15
(1) 3: "ReducedGradient"
||rGf||inf = 3.7462461296e-01
rGf_k =
5
0.374625:1 0.374464:2 0.374464:3 0.374464:4 0.374303:5
(1) 4.-1: "CheckSkipBFGSUpdate"
ratio = (skip_bfgs_prop_const/sqrt(||rGL_km1||+||c_km1||))*(||Zpz_km1||/||Ypy_km1||)
= (1.0000000000e+01/sqrt(2.4169862058e+01+6.4588832268e+03))
* (1.1032346914e+02/1.1999603325e+00)
= 1.1418557184e+01
ratio > 1
Perform BFGS update if you can ...
(1) 4: "ReducedHessian"
Performing Secant update ...
||y_bfgs||inf = 1.1183897541e+01
||s_bfgs||inf = 6.7559966523e-01
y_bfgs =
5
11.1832:1 11.1836:2 11.1836:3 11.1836:4 11.1839:5
s_bfgs =
5
0.675537:1 0.675568:2 0.675568:3 0.675568:4 0.6756:5
Rescaling the initial identity matrix before the update as:
Iscale = (y'*y)/(y'*s) = (6.2535947673e+02)/(3.7776268532e+01) = 1.6554294562e+01
B = Iscale * eye(n-r) ...
B after rescaling =
Unfactored symmetric matrix stored as lower triangle (ignore upper nonzeros):
5 5
16.5543:1:1 0:1:2 1:1:3 0:1:4 0:1:5
0:2:1 16.5543:2:2 0:2:3 1:2:4 0:2:5
0:3:1 0:3:2 16.5543:3:3 0:3:4 1:3:5
0:4:1 0:4:2 0:4:3 16.5543:4:4 0:4:5
0:5:1 0:5:2 0:5:3 0:5:4 16.5543:5:5
Considering the dampened update ...
s_bfgs'*y_bfgs = 3.7776268532e+01 >= s_bfgs' * B * s_bfgs = 3.7776268535e+01
Perform the undamped update ...
B after the BFGS update =
Unfactored symmetric matrix stored as lower triangle (ignore upper nonzeros):
5 5
16.5544:1:1 0:1:2 1:1:3 0:1:4 0:1:5
5.27915e-05:2:1 16.5543:2:2 0:2:3 1:2:4 0:2:5
5.27878e-05:3:1 1.1783e-08:3:2 16.5543:3:3 0:3:4 1:3:5
5.27841e-05:4:1 8.12156e-09:4:2 4.46017e-09:4:3 16.5543:4:4 0:4:5
-4.02538e-09:5:1 -5.27841e-05:5:2 -5.27878e-05:5:3 -5.27914e-05:5:4 16.5542:5:5
||rHL_k||inf = 1.6554558493e+01
cond_inf(rHL_k) = 1.0000318885e+00
rHL_k =
Unfactored symmetric matrix stored as lower triangle (ignore upper nonzeros):
5 5
16.5544:1:1 0:1:2 4.0687:1:3 2.85463e-09:1:4 1.95474e-09:1:5
5.27915e-05:2:1 16.5543:2:2 0:2:3 4.0687:2:4 1.05485e-09:2:5
5.27878e-05:3:1 1.1783e-08:3:2 16.5543:3:3 0:3:4 4.0687:3:5
5.27841e-05:4:1 8.12156e-09:4:2 4.46017e-09:4:3 16.5543:4:4 0:4:5
-4.02538e-09:5:1 -5.27841e-05:5:2 -5.27878e-05:5:3 -5.27914e-05:5:4 16.5542:5:5
Matrix scaling M = scale*U'*U, scale = 1
Upper cholesky factor U (ignore lower nonzeros):
5 5
4.06871:1:1 1.2975e-05:1:2 1.29741e-05:1:3 1.29732e-05:1:4 -9.8935e-10:1:5
0:2:1 4.0687:2:2 2.85463e-09:2:3 1.95474e-09:2:4 -1.29732e-05:2:5
16.5543:3:1 0:3:2 4.0687:3:3 1.05485e-09:3:4 -1.29741e-05:3:5
1.1783e-08:4:1 16.5543:4:2 0:4:3 4.0687:4:4 -1.2975e-05:4:5
8.12156e-09:5:1 4.46017e-09:5:2 16.5543:5:3 0:5:4 4.06868:5:5
(1) 5.-1: "SetDBoundsStd"
dl(var_indep)_k =
5
-0.742802:1 -0.742833:2 -0.742833:3 -0.742833:4 -0.742864:5
du(var_indep)_k =
5
1e+50:1 1e+50:2 1e+50:3 1e+50:4 1e+50:5
(1) 5: "TangentialStep"
qp_grad_k =
5
0.374625:1 0.374464:2 0.374464:3 0.374464:4 0.374303:5
Determine if we can use simple bounds on pz ...
m = 3000
dynamic_cast<const MatrixIdentConcat*>(&Z_k) = 0xe2c76b0
||Ypy_k(var_indep)||inf = 2.5901993894e-01
Using simple bounds on pz ...
There are no finite bounds on dependent variables. There will be no extra inequality constraints added on D*pz ...
Calling QPKWIK to solve QP problem ...
||pz_k||inf = 2.2629695306e-02
nu_k.nz() = 0
max(|nu_k(i)|) = 0.0000000000e+00
||Zpz_k||2 = 6.0331754008e-02
pz_k =
5
-0.0226297:1 -0.0226203:2 -0.0226203:3 -0.0226203:4 -0.022611:5
nu_k(var_indep) =
5
0:1 0:2 0:3 0:4 0:5
Zpz(var_indep)_k =
5
-0.0226297:1 -0.0226203:2 -0.0226203:3 -0.0226203:4 -0.022611:5
(1) 6: "CalcDFromYPYZPZ"
(Ypy_k'*Zpz_k)/(||Ypy_k||2 * ||Zpz_k||2 + eps)
= (-1.9637069748e-15)/(1.0621477516e+00 * 6.0331754008e-02 + 2.2250738585e-308)
= -3.0644024221e-14
||d_k||inf = 2.8163092161e-01
||d(var_dep)_k||inf = 1.5659094503e-02
||d(var_indep)_k||inf = 2.8163092161e-01
d(var_indep)_k =
5
-0.281457:1 -0.281544:2 -0.281544:3 -0.281544:4 -0.281631:5
(1) 7: "CalcReducedGradLagrangian"
||rGL_k||inf = 3.7462461296e-01
rGL_k =
5
0.374625:1 0.374464:2 0.374464:3 0.374464:4 0.374303:5
(1) 8: "CheckConvergence"
scale_opt_factor = 1.0000000000e+00 (scale_opt_error_by = SCALE_BY_ONE)
scale_feas_factor = 1.0000000000e+00 (scale_feas_error_by = SCALE_BY_ONE)
scale_comp_factor = 1.0000000000e+00 (scale_comp_error_by = SCALE_BY_ONE)
opt_scale_factor = 1.7428744836e+00 (scale_opt_error_by_Gf = true)
opt_kkt_err_k = 2.1494640979e-01 > opt_tol = 1.0000000000e-02
feas_kkt_err_k = 6.9682547090e+01 > feas_tol = 1.0000000000e-07
comp_kkt_err_k = -0.0000000000e+00 < comp_tol = 1.0000000000e-06
step_err = 1.6158990464e-01 > step_tol = 1.0000000000e-02
Have not found the solution yet, have to keep going (k = 1) :-(
(1) 9.-1: "LineSearchFullStep"
f_k = 2.1820737219e+00
||c_k||inf = 6.9682547090e+01
alpha_k = 1.0000000000e+00
||x_kp1||inf = 4.6135478069e-01
f_kp1 = 6.1576438692e-01
||c_kp1||inf = 1.5830011682e+01
(1) 9: "LineSearch"
theta_k = ||c_k||1/c_k.dim() = 6.8472167804e+01
f_min==F_MIN_UNBOUNDED: Setting gamma_f_used = gamma_f = 1.0000000000e-05.
Beginning Filter line search method.
Current Filter
-----------------------------------------------------
| f_with_boundary | theta_with_boundary |
-----------------------------------------------------
| 2.1813890002e+00 6.8471483083e+01|
Iteration Status
----------------------------------------------------------------------------------------------------------
| alpha_k | f_kp1 | theta_kp1 | pt. status | comment |
----------------------------------------------------------------------------------------------------------
|1.0000000000e+00 6.1576438692e-01 1.5552264182e+01 accepted Fraction Reduction (! Switch Cond )|
Point was accepted - augmenting the filter ...
Augmenting the filter with the point:
f_with_boundary = f_kp1 - gamma_f_used*theta_kp1 = 6.1576438692e-01 - 1.0000000000e-05*1.5552264182e+01 = 6.1560886428e-01
theta_with_boundary = (1-gamma_theta)*theta_kp1 = (1-1.0000000000e-05)*1.5552264182e+01 = 1.5552108660e+01
Removing from the filter the redundant point:
f_with_boundary = 2.1813890002e+00
theta_with_boundary = 6.8471483083e+01
iteration added = 0
(2) 1: "EvalNewPoint"
||x_k||inf = 4.6135478069e-01
||x(var_dep)_k||inf = 7.4771752444e-03
||x(var_indep)_k||inf = 4.6135478069e-01
x(var_indep)_k =
5
0.461355:1 0.461299:2 0.461299:3 0.461299:4 0.461244:5
Updating the decomposition ...
Updating the range/null decompostion matrices ...
***********************************************************
*** DecompositionSystemVarReductImp::update_decomp(...) ***
************************************************************
Warning!!! mat_rel != MATRICES_INDEP_IMPS; The decompsition matrix objects may not be independent of each other!
****************************************************************
*** DecompositionSystemVarReductImp::get_basis_matrices(...) ***
****************************************************************
Allocated a new explicit matrix object for D = -inv(C)*N of type 'AbstractLinAlgPack::MultiVectorMutableDense' ...
End DecompositionSystemVarReductImp::get_basis_matrices(...)
Updating the basis matrix C and other matices using the BasisSystem object ...
Using a direct sparse solver to update basis ...
Using LAPACK xGETRF to refactor the basis matrix ...
End DecompositionSystemVarReductImp::update_decomp(...)
Printing the updated iteration quantities ...
f_k = 6.1576438692e-01
||Gf_k||inf = 4.6135478069e-01
||Gf_k(var_dep)_k||inf = 7.4771752444e-03
||Gf_k(var_indep)_k||inf = 4.6135478069e-01
||c_k||inf = 1.5830011682e+01
Gf(var_indep)_k =
5
0.461355:1 0.461299:2 0.461299:3 0.461299:4 0.461244:5
(2) 2: "QuasiNormalStep"
||py|| = 7.0350662441e-03
||Ypy||2 = 3.9705009790e-01
(2) 2.1: "CheckDecompositionFromPy"
beta = ||py||/||c|| = 4.4441320608e-04
(2) 2.2: "CheckDecompositionFromRPy"
beta = ||R*py_k + c_k(decomp)||inf / (||c_k(decomp)||inf + small_number)
= 2.3092638912e-14 / (1.5830011682e+01 + 2.2250738585e-308)
= 1.4587884946e-15
(2) 3: "ReducedGradient"
||rGf||inf = 4.1554627380e-01
rGf_k =
5
0.415546:1 0.415437:2 0.415437:3 0.415437:4 0.415329:5
(2) 4.-1: "CheckSkipBFGSUpdate"
ratio = (skip_bfgs_prop_const/sqrt(||rGL_km1||+||c_km1||))*(||Zpz_km1||/||Ypy_km1||)
= (1.0000000000e+01/sqrt(8.3732647964e-01+3.7503756046e+03))
* (6.0331754008e-02/1.0621477516e+00)
= 9.2741722769e-03
ratio < 1
Skipping BFGS update ...
rHL_k = rHL_km1
(2) 4: "ReducedHessian"
The matrix rHL_k has already been updated so leave it
(2) 5.-1: "SetDBoundsStd"
dl(var_indep)_k =
5
-0.461345:1 -0.461289:2 -0.461289:3 -0.461289:4 -0.461234:5
du(var_indep)_k =
5
1e+50:1 1e+50:2 1e+50:3 1e+50:4 1e+50:5
(2) 5: "TangentialStep"
qp_grad_k =
5
0.415546:1 0.415437:2 0.415437:3 0.415437:4 0.415329:5
Determine if we can use simple bounds on pz ...
m = 3000
dynamic_cast<const MatrixIdentConcat*>(&Z_k) = 0xe2c76b0
||Ypy_k(var_indep)||inf = 4.3200066153e-02
Using simple bounds on pz ...
There are no finite bounds on dependent variables. There will be no extra inequality constraints added on D*pz ...
Calling QPKWIK to solve QP problem ...
||pz_k||inf = 2.5101622321e-02
nu_k.nz() = 0
max(|nu_k(i)|) = 0.0000000000e+00
||Zpz_k||2 = 5.7849459762e-02
pz_k =
5
-0.0251016:1 -0.0250955:2 -0.0250955:3 -0.0250955:4 -0.0250893:5
nu_k(var_indep) =
5
0:1 0:2 0:3 0:4 0:5
Zpz(var_indep)_k =
5
-0.0251016:1 -0.0250955:2 -0.0250955:3 -0.0250955:4 -0.0250893:5
(2) 6: "CalcDFromYPYZPZ"
(Ypy_k'*Zpz_k)/(||Ypy_k||2 * ||Zpz_k||2 + eps)
= (-3.2656169435e-16)/(3.9705009790e-01 * 5.7849459762e-02 + 2.2250738585e-308)
= -1.4217414516e-14
||d_k||inf = 6.8289342521e-02
||d(var_dep)_k||inf = 6.7783028666e-03
||d(var_indep)_k||inf = 6.8289342521e-02
d(var_indep)_k =
5
-0.0682077:1 -0.0682485:2 -0.0682485:3 -0.0682485:4 -0.0682893:5
(2) 7: "CalcReducedGradLagrangian"
||rGL_k||inf = 4.1554627380e-01
rGL_k =
5
0.415546:1 0.415437:2 0.415437:3 0.415437:4 0.415329:5
(2) 8: "CheckConvergence"
scale_opt_factor = 1.0000000000e+00 (scale_opt_error_by = SCALE_BY_ONE)
scale_feas_factor = 1.0000000000e+00 (scale_feas_error_by = SCALE_BY_ONE)
scale_comp_factor = 1.0000000000e+00 (scale_comp_error_by = SCALE_BY_ONE)
opt_scale_factor = 1.4613547807e+00 (scale_opt_error_by_Gf = true)
opt_kkt_err_k = 2.8435687164e-01 > opt_tol = 1.0000000000e-02
feas_kkt_err_k = 1.5830011682e+01 > feas_tol = 1.0000000000e-07
comp_kkt_err_k = -0.0000000000e+00 < comp_tol = 1.0000000000e-06
step_err = 4.6733716607e-02 > step_tol = 1.0000000000e-02
Have not found the solution yet, have to keep going (k = 2) :-(
(2) 9.-1: "LineSearchFullStep"
f_k = 6.1576438692e-01
||c_k||inf = 1.5830011682e+01
alpha_k = 1.0000000000e+00
||x_kp1||inf = 3.9314710830e-01
f_kp1 = 3.8695300275e-01
||c_kp1||inf = 1.3445285133e+00
(2) 9: "LineSearch"
theta_k = ||c_k||1/c_k.dim() = 1.5552264182e+01
f_min==F_MIN_UNBOUNDED: Setting gamma_f_used = gamma_f = 1.0000000000e-05.
Beginning Filter line search method.
Current Filter
-----------------------------------------------------
| f_with_boundary | theta_with_boundary |
-----------------------------------------------------
| 6.1560886428e-01 1.5552108660e+01|
Iteration Status
----------------------------------------------------------------------------------------------------------
| alpha_k | f_kp1 | theta_kp1 | pt. status | comment |
----------------------------------------------------------------------------------------------------------
|1.0000000000e+00 3.8695300275e-01 1.3201800917e+00 accepted Fraction Reduction (! Switch Cond )|
Point was accepted - augmenting the filter ...
Augmenting the filter with the point:
f_with_boundary = f_kp1 - gamma_f_used*theta_kp1 = 3.8695300275e-01 - 1.0000000000e-05*1.3201800917e+00 = 3.8693980095e-01
theta_with_boundary = (1-gamma_theta)*theta_kp1 = (1-1.0000000000e-05)*1.3201800917e+00 = 1.3201668899e+00
Removing from the filter the redundant point:
f_with_boundary = 6.1560886428e-01
theta_with_boundary = 1.5552108660e+01
iteration added = 1
(3) 1: "EvalNewPoint"
||x_k||inf = 3.9314710830e-01
||x(var_dep)_k||inf = 6.9887237779e-04
||x(var_indep)_k||inf = 3.9314710830e-01
x(var_indep)_k =
5
0.393147:1 0.393051:2 0.393051:3 0.393051:4 0.392954:5
Updating the decomposition ...
Updating the range/null decompostion matrices ...
***********************************************************
*** DecompositionSystemVarReductImp::update_decomp(...) ***
************************************************************
Warning!!! mat_rel != MATRICES_INDEP_IMPS; The decompsition matrix objects may not be independent of each other!
****************************************************************
*** DecompositionSystemVarReductImp::get_basis_matrices(...) ***
****************************************************************
Allocated a new explicit matrix object for D = -inv(C)*N of type 'AbstractLinAlgPack::MultiVectorMutableDense' ...
End DecompositionSystemVarReductImp::get_basis_matrices(...)
Updating the basis matrix C and other matices using the BasisSystem object ...
Using a direct sparse solver to update basis ...
Using LAPACK xGETRF to refactor the basis matrix ...
End DecompositionSystemVarReductImp::update_decomp(...)
Printing the updated iteration quantities ...
f_k = 3.8695300275e-01
||Gf_k||inf = 3.9314710830e-01
||Gf_k(var_dep)_k||inf = 6.9887237779e-04
||Gf_k(var_indep)_k||inf = 3.9314710830e-01
||c_k||inf = 1.3445285133e+00
Gf(var_indep)_k =
5
0.393147:1 0.393051:2 0.393051:3 0.393051:4 0.392954:5
(3) 2: "QuasiNormalStep"
||py|| = 6.9845040071e-04
||Ypy||2 = 3.8222397636e-02
(3) 2.1: "CheckDecompositionFromPy"
beta = ||py||/||c|| = 5.1947607941e-04
(3) 2.2: "CheckDecompositionFromRPy"
beta = ||R*py_k + c_k(decomp)||inf / (||c_k(decomp)||inf + small_number)
= 1.1102230246e-15 / (1.3445285133e+00 + 2.2250738585e-308)
= 8.2573408721e-16
(3) 3: "ReducedGradient"
||rGf||inf = 3.9272839189e-01
rGf_k =
5
0.392728:1 0.392631:2 0.392631:3 0.392631:4 0.392533:5
(3) 4.-1: "CheckSkipBFGSUpdate"
ratio = (skip_bfgs_prop_const/sqrt(||rGL_km1||+||c_km1||))*(||Zpz_km1||/||Ypy_km1||)
= (1.0000000000e+01/sqrt(9.2894644415e-01+8.5183273306e+02))
* (5.7849459762e-02/3.9705009790e-01)
= 4.9893062465e-02
ratio < 1
Skipping BFGS update ...
rHL_k = rHL_km1
(3) 4: "ReducedHessian"
The matrix rHL_k has already been updated so leave it
(3) 5.-1: "SetDBoundsStd"
dl(var_indep)_k =
5
-0.393137:1 -0.393041:2 -0.393041:3 -0.393041:4 -0.392944:5
du(var_indep)_k =
5
1e+50:1 1e+50:2 1e+50:3 1e+50:4 1e+50:5
(3) 5: "TangentialStep"
qp_grad_k =
5
0.392728:1 0.392631:2 0.392631:3 0.392631:4 0.392533:5
Determine if we can use simple bounds on pz ...
m = 3000
dynamic_cast<const MatrixIdentConcat*>(&Z_k) = 0xe2c76b0
||Ypy_k(var_indep)||inf = 4.2053082371e-04
Using simple bounds on pz ...
There are no finite bounds on dependent variables. There will be no extra inequality constraints added on D*pz ...
Calling QPKWIK to solve QP problem ...
||pz_k||inf = 2.3723277979e-02
nu_k.nz() = 0
max(|nu_k(i)|) = 0.0000000000e+00
||Zpz_k||2 = 5.3050520400e-02
pz_k =
5
-0.0237233:1 -0.0237178:2 -0.0237178:3 -0.0237178:4 -0.0237123:5
nu_k(var_indep) =
5
0:1 0:2 0:3 0:4 0:5
Zpz(var_indep)_k =
5
-0.0237233:1 -0.0237178:2 -0.0237178:3 -0.0237178:4 -0.0237123:5
(3) 6: "CalcDFromYPYZPZ"
(Ypy_k'*Zpz_k)/(||Ypy_k||2 * ||Zpz_k||2 + eps)
= (-9.2326591251e-19)/(3.8222397636e-02 * 5.3050520400e-02 + 2.2250738585e-308)
= -4.5532262059e-16
||d_k||inf = 2.4141742846e-02
||d(var_dep)_k||inf = 6.7465659398e-04
||d(var_indep)_k||inf = 2.4141742846e-02
d(var_indep)_k =
5
-0.0241417:1 -0.0241373:2 -0.0241373:3 -0.0241373:4 -0.0241328:5
(3) 7: "CalcReducedGradLagrangian"
||rGL_k||inf = 3.9272839189e-01
rGL_k =
5
0.392728:1 0.392631:2 0.392631:3 0.392631:4 0.392533:5
(3) 8: "CheckConvergence"
scale_opt_factor = 1.0000000000e+00 (scale_opt_error_by = SCALE_BY_ONE)
scale_feas_factor = 1.0000000000e+00 (scale_feas_error_by = SCALE_BY_ONE)
scale_comp_factor = 1.0000000000e+00 (scale_comp_error_by = SCALE_BY_ONE)
opt_scale_factor = 1.3931471083e+00 (scale_opt_error_by_Gf = true)
opt_kkt_err_k = 2.8190015939e-01 > opt_tol = 1.0000000000e-02
feas_kkt_err_k = 1.3445285133e+00 > feas_tol = 1.0000000000e-07
comp_kkt_err_k = -0.0000000000e+00 < comp_tol = 1.0000000000e-06
step_err = 1.7328925784e-02 > step_tol = 1.0000000000e-02
Have not found the solution yet, have to keep going (k = 3) :-(
(3) 9.-1: "LineSearchFullStep"
f_k = 3.8695300275e-01
||c_k||inf = 1.3445285133e+00
alpha_k = 1.0000000000e+00
||x_kp1||inf = 3.6900536545e-01
f_kp1 = 3.4024364074e-01
||c_kp1||inf = 4.4987367193e-02
(3) 9: "LineSearch"
theta_k = ||c_k||1/c_k.dim() = 1.3201800917e+00
f_min==F_MIN_UNBOUNDED: Setting gamma_f_used = gamma_f = 1.0000000000e-05.
Beginning Filter line search method.
Current Filter
-----------------------------------------------------
| f_with_boundary | theta_with_boundary |
-----------------------------------------------------
| 3.8693980095e-01 1.3201668899e+00|
Iteration Status
----------------------------------------------------------------------------------------------------------
| alpha_k | f_kp1 | theta_kp1 | pt. status | comment |
----------------------------------------------------------------------------------------------------------
|1.0000000000e+00 3.4024364074e-01 4.4177631526e-02 accepted Fraction Reduction (! Switch Cond )|
Point was accepted - augmenting the filter ...
Augmenting the filter with the point:
f_with_boundary = f_kp1 - gamma_f_used*theta_kp1 = 3.4024364074e-01 - 1.0000000000e-05*4.4177631526e-02 = 3.4024319897e-01
theta_with_boundary = (1-gamma_theta)*theta_kp1 = (1-1.0000000000e-05)*4.4177631526e-02 = 4.4177189749e-02
Removing from the filter the redundant point:
f_with_boundary = 3.8693980095e-01
theta_with_boundary = 1.3201668899e+00
iteration added = 2
(4) 1: "EvalNewPoint"
||x_k||inf = 3.6900536545e-01
||x(var_dep)_k||inf = 2.4215783810e-05
||x(var_indep)_k||inf = 3.6900536545e-01
x(var_indep)_k =
5
0.369005:1 0.368913:2 0.368913:3 0.368913:4 0.368821:5
Updating the decomposition ...
Updating the range/null decompostion matrices ...
***********************************************************
*** DecompositionSystemVarReductImp::update_decomp(...) ***
************************************************************
Warning!!! mat_rel != MATRICES_INDEP_IMPS; The decompsition matrix objects may not be independent of each other!
****************************************************************
*** DecompositionSystemVarReductImp::get_basis_matrices(...) ***
****************************************************************
Allocated a new explicit matrix object for D = -inv(C)*N of type 'AbstractLinAlgPack::MultiVectorMutableDense' ...
End DecompositionSystemVarReductImp::get_basis_matrices(...)
Updating the basis matrix C and other matices using the BasisSystem object ...
Using a direct sparse solver to update basis ...
Using LAPACK xGETRF to refactor the basis matrix ...
End DecompositionSystemVarReductImp::update_decomp(...)
Printing the updated iteration quantities ...
f_k = 3.4024364074e-01
||Gf_k||inf = 3.6900536545e-01
||Gf_k(var_dep)_k||inf = 2.4215783810e-05
||Gf_k(var_indep)_k||inf = 3.6900536545e-01
||c_k||inf = 4.4987367193e-02
Gf(var_indep)_k =
5
0.369005:1 0.368913:2 0.368913:3 0.368913:4 0.368821:5
(4) 2: "QuasiNormalStep"
||py|| = 2.4215765620e-05
||Ypy||2 = 1.3249505872e-03
(4) 2.1: "CheckDecompositionFromPy"
beta = ||py||/||c|| = 5.3827923550e-04
(4) 2.2: "CheckDecompositionFromRPy"
beta = ||R*py_k + c_k(decomp)||inf / (||c_k(decomp)||inf + small_number)
= 4.1633363423e-17 / (4.4987367193e-02 + 2.2250738585e-308)
= 9.2544565333e-16
(4) 3: "ReducedGradient"
||rGf||inf = 3.6900485363e-01
rGf_k =
5
0.369005:1 0.368913:2 0.368913:3 0.368913:4 0.368821:5
(4) 4.-1: "CheckSkipBFGSUpdate"
ratio = (skip_bfgs_prop_const/sqrt(||rGL_km1||+||c_km1||))*(||Zpz_km1||/||Ypy_km1||)
= (1.0000000000e+01/sqrt(8.7794944328e-01+7.2309266475e+01))
* (5.3050520400e-02/3.8222397636e-02)
= 1.6223856969e+00
ratio > 1
Perform BFGS update if you can ...
(4) 4: "ReducedHessian"
Performing Secant update ...
||y_bfgs||inf = 2.3723538254e-02
||s_bfgs||inf = 2.3723277979e-02
y_bfgs =
5
-0.0237235:1 -0.023718:2 -0.023718:3 -0.023718:4 -0.0237125:5
s_bfgs =
5
-0.0237233:1 -0.0237178:2 -0.0237178:3 -0.0237178:4 -0.0237123:5
Considering the dampened update ...
s_bfgs'*y_bfgs = 2.8126935606e-03 < s_bfgs' * B * s_bfgs = 4.6561647149e-02
Dampen the update ...
theta = 8.5143334100e-01
y_bfgs = theta*y_bfgs + (1-theta)*B*s_bfgs ...
||y_bfgs||inf = 7.8545356511e-02
y_bfgs =
5
-0.0785454:1 -0.0785262:2 -0.0785262:3 -0.0785262:4 -0.078507:5
B after the BFGS update =
Unfactored symmetric matrix stored as lower triangle (ignore upper nonzeros):
5 5
13.9044:1:1 0:1:2 4.0687:1:3 2.85463e-09:1:4 1.95474e-09:1:5
-2.64929:2:1 13.9056:2:2 0:2:3 4.0687:2:4 1.05485e-09:2:5
-2.64929:3:1 -2.64869:3:2 13.9056:3:3 0:3:4 4.0687:3:5
-2.64929:4:1 -2.64869:4:2 -2.64869:4:3 13.9056:4:4 0:4:5
-2.64869:5:1 -2.64808:5:2 -2.64808:5:3 -2.64808:5:4 13.9068:5:5
||rHL_k||inf = 2.4499747866e+01
cond_inf(rHL_k) = 7.4011738690e+00
rHL_k =
Unfactored symmetric matrix stored as lower triangle (ignore upper nonzeros):
5 5
13.9044:1:1 0:1:2 3.66071:1:3 -0.861437:1:4 -0.861437:1:5
-2.64929:2:1 13.9056:2:2 0:2:3 3.55791:2:4 -1.0949:2:5
-2.64929:3:1 -2.64869:3:2 13.9056:3:3 0:3:4 3.38525:3:5
-2.64929:4:1 -2.64869:4:2 -2.64869:4:3 13.9056:4:4 0:4:5
-2.64869:5:1 -2.64808:5:2 -2.64808:5:3 -2.64808:5:4 13.9068:5:5
Matrix scaling M = scale*U'*U, scale = 1
Upper cholesky factor U (ignore lower nonzeros):
5 5
3.72886:1:1 -0.710484:1:2 -0.710484:1:3 -0.710484:1:4 -0.710321:1:5
0:2:1 3.66071:2:2 -0.861437:2:3 -0.861437:2:4 -0.86124:2:5
13.9056:3:1 0:3:2 3.55791:3:3 -1.0949:3:4 -1.09465:3:5
-2.64869:4:1 13.9056:4:2 0:4:3 3.38525:4:4 -1.50452:4:5
-2.64869:5:1 -2.64869:5:2 13.9056:5:3 0:5:4 3.03294:5:5
(4) 5.-1: "SetDBoundsStd"
dl(var_indep)_k =
5
-0.368995:1 -0.368903:2 -0.368903:3 -0.368903:4 -0.368811:5
du(var_indep)_k =
5
1e+50:1 1e+50:2 1e+50:3 1e+50:4 1e+50:5
(4) 5: "TangentialStep"
qp_grad_k =
5
0.369005:1 0.368913:2 0.368913:3 0.368913:4 0.368821:5
Determine if we can use simple bounds on pz ...
m = 3000
dynamic_cast<const MatrixIdentConcat*>(&Z_k) = 0xe2c76b0
||Ypy_k(var_indep)||inf = 5.1410422885e-07
Using simple bounds on pz ...
There are no finite bounds on dependent variables. There will be no extra inequality constraints added on D*pz ...
Calling QPKWIK to solve QP problem ...
||pz_k||inf = 1.1145113136e-01
nu_k.nz() = 0
max(|nu_k(i)|) = 0.0000000000e+00
||Zpz_k||2 = 2.4915426691e-01
pz_k =
5
-0.111451:1 -0.111425:2 -0.111425:3 -0.111425:4 -0.111399:5
nu_k(var_indep) =
5
0:1 0:2 0:3 0:4 0:5
Zpz(var_indep)_k =
5
-0.111451:1 -0.111425:2 -0.111425:3 -0.111425:4 -0.111399:5
(4) 6: "CalcDFromYPYZPZ"
(Ypy_k'*Zpz_k)/(||Ypy_k||2 * ||Zpz_k||2 + eps)
= (-1.0164395367e-20)/(1.3249505872e-03 * 2.4915426691e-01 + 2.2250738585e-308)
= -3.0790272924e-17
||d_k||inf = 1.1145164318e-01
||d(var_dep)_k||inf = 2.0274247521e-05
||d(var_indep)_k||inf = 1.1145164318e-01
d(var_indep)_k =
5
-0.111452:1 -0.111426:2 -0.111426:3 -0.111426:4 -0.1114:5
(4) 7: "CalcReducedGradLagrangian"
||rGL_k||inf = 3.6900485363e-01
rGL_k =
5
0.369005:1 0.368913:2 0.368913:3 0.368913:4 0.368821:5
(4) 8: "CheckConvergence"
scale_opt_factor = 1.0000000000e+00 (scale_opt_error_by = SCALE_BY_ONE)
scale_feas_factor = 1.0000000000e+00 (scale_feas_error_by = SCALE_BY_ONE)
scale_comp_factor = 1.0000000000e+00 (scale_comp_error_by = SCALE_BY_ONE)
opt_scale_factor = 1.3690053654e+00 (scale_opt_error_by_Gf = true)
opt_kkt_err_k = 2.6954229906e-01 > opt_tol = 1.0000000000e-02
feas_kkt_err_k = 4.4987367193e-02 > feas_tol = 1.0000000000e-07
comp_kkt_err_k = -0.0000000000e+00 < comp_tol = 1.0000000000e-06
step_err = 8.1410669372e-02 > step_tol = 1.0000000000e-02
Have not found the solution yet, have to keep going (k = 4) :-(
(4) 9.-1: "LineSearchFullStep"
f_k = 3.4024364074e-01
||c_k||inf = 4.4987367193e-02
alpha_k = 1.0000000000e+00
||x_kp1||inf = 2.5755372227e-01
f_kp1 = 1.6574989579e-01
||c_kp1||inf = 6.1791102848e-03
(4) 9: "LineSearch"
theta_k = ||c_k||1/c_k.dim() = 4.4177631526e-02
f_min==F_MIN_UNBOUNDED: Setting gamma_f_used = gamma_f = 1.0000000000e-05.
Beginning Filter line search method.
Current Filter
-----------------------------------------------------
| f_with_boundary | theta_with_boundary |
-----------------------------------------------------
| 3.4024319897e-01 4.4177189749e-02|
Iteration Status
----------------------------------------------------------------------------------------------------------
| alpha_k | f_kp1 | theta_kp1 | pt. status | comment |
----------------------------------------------------------------------------------------------------------
|1.0000000000e+00 1.6574989579e-01 6.0687208500e-03 accepted Fraction Reduction (! Switch Cond )|
Point was accepted - augmenting the filter ...
Augmenting the filter with the point:
f_with_boundary = f_kp1 - gamma_f_used*theta_kp1 = 1.6574989579e-01 - 1.0000000000e-05*6.0687208500e-03 = 1.6574983511e-01
theta_with_boundary = (1-gamma_theta)*theta_kp1 = (1-1.0000000000e-05)*6.0687208500e-03 = 6.0686601628e-03
Removing from the filter the redundant point:
f_with_boundary = 3.4024319897e-01
theta_with_boundary = 4.4177189749e-02
iteration added = 3
(5) 1: "EvalNewPoint"
||x_k||inf = 2.5755372227e-01
||x(var_dep)_k||inf = 3.9415362886e-06
||x(var_indep)_k||inf = 2.5755372227e-01
x(var_indep)_k =
5
0.257554:1 0.257488:2 0.257488:3 0.257488:4 0.257422:5
Updating the decomposition ...
Updating the range/null decompostion matrices ...
***********************************************************
*** DecompositionSystemVarReductImp::update_decomp(...) ***
************************************************************
Warning!!! mat_rel != MATRICES_INDEP_IMPS; The decompsition matrix objects may not be independent of each other!
****************************************************************
*** DecompositionSystemVarReductImp::get_basis_matrices(...) ***
****************************************************************
Allocated a new explicit matrix object for D = -inv(C)*N of type 'AbstractLinAlgPack::MultiVectorMutableDense' ...
End DecompositionSystemVarReductImp::get_basis_matrices(...)
Updating the basis matrix C and other matices using the BasisSystem object ...
Using a direct sparse solver to update basis ...
Using LAPACK xGETRF to refactor the basis matrix ...
End DecompositionSystemVarReductImp::update_decomp(...)
Printing the updated iteration quantities ...
f_k = 1.6574989579e-01
||Gf_k||inf = 2.5755372227e-01
||Gf_k(var_dep)_k||inf = 3.9415362886e-06
||Gf_k(var_indep)_k||inf = 2.5755372227e-01
||c_k||inf = 6.1791102848e-03
Gf(var_indep)_k =
5
0.257554:1 0.257488:2 0.257488:3 0.257488:4 0.257422:5
(5) 2: "QuasiNormalStep"
||py|| = 3.9415361956e-06
||Ypy||2 = 2.1569444240e-04
(5) 2.1: "CheckDecompositionFromPy"
beta = ||py||/||c|| = 6.3788086213e-04
(5) 2.2: "CheckDecompositionFromRPy"
beta = ||R*py_k + c_k(decomp)||inf / (||c_k(decomp)||inf + small_number)
= 6.0715321659e-18 / (6.1791102848e-03 + 2.2250738585e-308)
= 9.8259003094e-16
(5) 3: "ReducedGradient"
||rGf||inf = 2.5755370750e-01
rGf_k =
5
0.257554:1 0.257488:2 0.257488:3 0.257488:4 0.257422:5
(5) 4.-1: "CheckSkipBFGSUpdate"
ratio = (skip_bfgs_prop_const/sqrt(||rGL_km1||+||c_km1||))*(||Zpz_km1||/||Ypy_km1||)
= (1.0000000000e+01/sqrt(8.2491431895e-01+2.4197092553e+00))
* (2.4915426691e-01/1.3249505872e-03)
= 1.0439663191e+03
ratio > 1
Perform BFGS update if you can ...
(5) 4: "ReducedHessian"
Performing Secant update ...
||y_bfgs||inf = 1.1145114613e-01
||s_bfgs||inf = 1.1145113136e-01
y_bfgs =
5
-0.111451:1 -0.111425:2 -0.111425:3 -0.111425:4 -0.111399:5
s_bfgs =
5
-0.111451:1 -0.111425:2 -0.111425:3 -0.111425:4 -0.111399:5
Considering the dampened update ...
s_bfgs'*y_bfgs = 6.2077810439e-02 >= s_bfgs' * B * s_bfgs = 2.0553084537e-01
Perform the undamped update ...
B after the BFGS update =
Unfactored symmetric matrix stored as lower triangle (ignore upper nonzeros):
5 5
13.442:1:1 0:1:2 3.66071:1:3 -0.861437:1:4 -0.861437:1:5
-3.11158:2:1 13.4434:2:2 0:2:3 3.55791:2:4 -1.0949:2:5
-3.11158:3:1 -3.11086:3:2 13.4434:3:3 0:3:4 3.38525:3:5
-3.11158:4:1 -3.11086:4:2 -3.11086:4:3 13.4434:4:4 0:4:5
-3.11086:5:1 -3.11013:5:2 -3.11013:5:3 -3.11013:5:4 13.4449:5:5
||rHL_k||inf = 2.5886144627e+01
cond_inf(rHL_k) = 2.5891815803e+01
rHL_k =
Unfactored symmetric matrix stored as lower triangle (ignore upper nonzeros):
5 5
13.442:1:1 0:1:2 3.56695:1:3 -1.07406:1:4 -1.07406:1:5
-3.11158:2:1 13.4434:2:2 0:2:3 3.4014:2:4 -1.4655:2:5
-3.11158:3:1 -3.11086:3:2 13.4434:3:3 0:3:4 3.0695:3:5
-3.11158:4:1 -3.11086:4:2 -3.11086:4:3 13.4434:4:4 0:4:5
-3.11086:5:1 -3.11013:5:2 -3.11013:5:3 -3.11013:5:4 13.4449:5:5
Matrix scaling M = scale*U'*U, scale = 1
Upper cholesky factor U (ignore lower nonzeros):
5 5
3.66633:1:1 -0.848692:1:2 -0.848692:1:3 -0.848692:1:4 -0.848494:1:5
0:2:1 3.56695:2:2 -1.07406:2:3 -1.07406:2:4 -1.07381:2:5
13.4434:3:1 0:3:2 3.4014:3:3 -1.4655:3:4 -1.46516:3:5
-3.11086:4:1 13.4434:4:2 0:4:3 3.0695:4:4 -2.3231:4:5
-3.11086:5:1 -3.11086:5:2 13.4434:5:3 0:5:4 2.00709:5:5
(5) 5.-1: "SetDBoundsStd"
dl(var_indep)_k =
5
-0.257544:1 -0.257478:2 -0.257478:3 -0.257478:4 -0.257412:5
du(var_indep)_k =
5
1e+50:1 1e+50:2 1e+50:3 1e+50:4 1e+50:5
(5) 5: "TangentialStep"
qp_grad_k =
5
0.257554:1 0.257488:2 0.257488:3 0.257488:4 0.257422:5
Determine if we can use simple bounds on pz ...
m = 3000
dynamic_cast<const MatrixIdentConcat*>(&Z_k) = 0xe2c76b0
||Ypy_k(var_indep)||inf = 1.4826932622e-08
Using simple bounds on pz ...
There are no finite bounds on dependent variables. There will be no extra inequality constraints added on D*pz ...
Calling QPKWIK to solve QP problem ...
||pz_k||inf = 2.5753641905e-01
nu_k.nz() = 1
max(|nu_k(i)|) = 6.2413617790e-05
||Zpz_k||2 = 5.7573213689e-01
pz_k =
5
-0.257536:1 -0.257476:2 -0.257476:3 -0.257476:4 -0.257412:5
nu_k(var_indep) =
5
0:1 0:2 0:3 0:4 -6.24136e-05:5
Zpz(var_indep)_k =
5
-0.257536:1 -0.257476:2 -0.257476:3 -0.257476:4 -0.257412:5
(5) 6: "CalcDFromYPYZPZ"
(Ypy_k'*Zpz_k)/(||Ypy_k||2 * ||Zpz_k||2 + eps)
= (4.9217246447e-22)/(2.1569444240e-04 * 5.7573213689e-01 + 2.2250738585e-308)
= 3.9633085606e-18
||d_k||inf = 2.5753643382e-01
||d(var_dep)_k||inf = 2.3277613186e-06
||d(var_indep)_k||inf = 2.5753643382e-01
d(var_indep)_k =
5
-0.257536:1 -0.257476:2 -0.257476:3 -0.257476:4 -0.257412:5
(5) 7: "CalcReducedGradLagrangian"
rGL_k =
5
0.257554:1 0.257488:2 0.257488:3 0.257488:4 0.257359:5
||rGL_k||inf = 2.5755370750e-01
rGL_k =
5
0.257554:1 0.257488:2 0.257488:3 0.257488:4 0.257359:5
(5) 8: "CheckConvergence"
scale_opt_factor = 1.0000000000e+00 (scale_opt_error_by = SCALE_BY_ONE)
scale_feas_factor = 1.0000000000e+00 (scale_feas_error_by = SCALE_BY_ONE)
scale_comp_factor = 1.0000000000e+00 (scale_comp_error_by = SCALE_BY_ONE)
opt_scale_factor = 1.2575537223e+00 (scale_opt_error_by_Gf = true)
opt_kkt_err_k = 2.0480533192e-01 > opt_tol = 1.0000000000e-02
feas_kkt_err_k = 6.1791102848e-03 > feas_tol = 1.0000000000e-07
comp_kkt_err_k = 1.6066000963e-05 > comp_tol = 1.0000000000e-06
step_err = 2.0479159598e-01 > step_tol = 1.0000000000e-02
Have not found the solution yet, have to keep going (k = 5) :-(
(5) 9.-1: "LineSearchFullStep"
f_k = 1.6574989579e-01
||c_k||inf = 6.1791102848e-03
alpha_k = 1.0000000000e+00
||x_kp1||inf = 1.7288455117e-05
f_kp1 = 4.3078479209e-09
||c_kp1||inf = 1.6001110173e-03
(5) 9: "LineSearch"
theta_k = ||c_k||1/c_k.dim() = 6.0687208500e-03
f_min==F_MIN_UNBOUNDED: Setting gamma_f_used = gamma_f = 1.0000000000e-05.
Beginning Filter line search method.
Current Filter
-----------------------------------------------------
| f_with_boundary | theta_with_boundary |
-----------------------------------------------------
| 1.6574983511e-01 6.0686601628e-03|
Iteration Status
----------------------------------------------------------------------------------------------------------
| alpha_k | f_kp1 | theta_kp1 | pt. status | comment |
----------------------------------------------------------------------------------------------------------
|1.0000000000e+00 4.3078479209e-09 1.5716730031e-03 accepted Fraction Reduction (! Switch Cond )|
Point was accepted - augmenting the filter ...
Augmenting the filter with the point:
f_with_boundary = f_kp1 - gamma_f_used*theta_kp1 = 4.3078479209e-09 - 1.0000000000e-05*1.5716730031e-03 = -1.1408882110e-08
theta_with_boundary = (1-gamma_theta)*theta_kp1 = (1-1.0000000000e-05)*1.5716730031e-03 = 1.5716572864e-03
Removing from the filter the redundant point:
f_with_boundary = 1.6574983511e-01
theta_with_boundary = 6.0686601628e-03
iteration added = 4
(6) 1: "EvalNewPoint"
||x_k||inf = 1.7288455117e-05
||x(var_dep)_k||inf = 1.6137749700e-06
||x(var_indep)_k||inf = 1.7288455117e-05
x(var_indep)_k =
5
1.72885e-05:1 1.17603e-05:2 1.176e-05:3 1.17596e-05:4 1e-05:5
Updating the decomposition ...
Updating the range/null decompostion matrices ...
***********************************************************
*** DecompositionSystemVarReductImp::update_decomp(...) ***
************************************************************
Warning!!! mat_rel != MATRICES_INDEP_IMPS; The decompsition matrix objects may not be independent of each other!
****************************************************************
*** DecompositionSystemVarReductImp::get_basis_matrices(...) ***
****************************************************************
Allocated a new explicit matrix object for D = -inv(C)*N of type 'AbstractLinAlgPack::MultiVectorMutableDense' ...
End DecompositionSystemVarReductImp::get_basis_matrices(...)
Updating the basis matrix C and other matices using the BasisSystem object ...
Using a direct sparse solver to update basis ...
Using LAPACK xGETRF to refactor the basis matrix ...
End DecompositionSystemVarReductImp::update_decomp(...)
Printing the updated iteration quantities ...
f_k = 4.3078479209e-09
||Gf_k||inf = 1.7288455117e-05
||Gf_k(var_dep)_k||inf = 1.6137749700e-06
||Gf_k(var_indep)_k||inf = 1.7288455117e-05
||c_k||inf = 1.6001110173e-03
Gf(var_indep)_k =
5
1.72885e-05:1 1.17603e-05:2 1.176e-05:3 1.17596e-05:4 1e-05:5
(6) 2: "QuasiNormalStep"
||py|| = 1.6137749599e-06
||Ypy||2 = 8.8328450816e-05
(6) 2.1: "CheckDecompositionFromPy"
beta = ||py||/||c|| = 1.0085393716e-03
(6) 2.2: "CheckDecompositionFromRPy"
beta = ||R*py_k + c_k(decomp)||inf / (||c_k(decomp)||inf + small_number)
= 1.3010426070e-18 / (1.6001110173e-03 + 2.2250738585e-308)
= 8.1309521210e-16
(6) 3: "ReducedGradient"
||rGf||inf = 1.7285338958e-05
rGf_k =
5
1.72853e-05:1 1.17572e-05:2 1.17568e-05:3 1.17565e-05:4 9.99687e-06:5
(6) 4.-1: "CheckSkipBFGSUpdate"
ratio = (skip_bfgs_prop_const/sqrt(||rGL_km1||+||c_km1||))*(||Zpz_km1||/||Ypy_km1||)
= (1.0000000000e+01/sqrt(5.7573220998e-01+3.3239761380e-01))
* (5.7573213689e-01/2.1569444240e-04)
= 2.8009641333e+04
ratio > 1
Perform BFGS update if you can ...
(6) 4: "ReducedHessian"
Performing Secant update ...
||y_bfgs||inf = 2.5753642216e-01
||s_bfgs||inf = 2.5753641905e-01
y_bfgs =
5
-0.257536:1 -0.257476:2 -0.257476:3 -0.257476:4 -0.257412:5
s_bfgs =
5
-0.257536:1 -0.257476:2 -0.257476:3 -0.257476:4 -0.257412:5
Considering the dampened update ...
s_bfgs'*y_bfgs = 3.3146748967e-01 >= s_bfgs' * B * s_bfgs = 3.3146752990e-01
Perform the undamped update ...
B after the BFGS update =
Unfactored symmetric matrix stored as lower triangle (ignore upper nonzeros):
5 5
13.442:1:1 0:1:2 3.56695:1:3 -1.07406:1:4 -1.07406:1:5
-3.11161:2:1 13.4434:2:2 0:2:3 3.4014:2:4 -1.4655:2:5
-3.11161:3:1 -3.11088:3:2 13.4434:3:3 0:3:4 3.0695:3:5
-3.11161:4:1 -3.11088:4:2 -3.11088:4:3 13.4434:4:4 0:4:5
-3.11083:5:1 -3.1101:5:2 -3.1101:5:3 -3.1101:5:4 13.445:5:5
||rHL_k||inf = 2.5886103889e+01
cond_inf(rHL_k) = 2.5891882950e+01
rHL_k =
Unfactored symmetric matrix stored as lower triangle (ignore upper nonzeros):
5 5
13.442:1:1 0:1:2 3.56695:1:3 -1.07407:1:4 -1.07407:1:5
-3.11161:2:1 13.4434:2:2 0:2:3 3.4014:2:4 -1.46552:2:5
-3.11161:3:1 -3.11088:3:2 13.4434:3:3 0:3:4 3.06949:3:5
-3.11161:4:1 -3.11088:4:2 -3.11088:4:3 13.4434:4:4 0:4:5
-3.11083:5:1 -3.1101:5:2 -3.1101:5:3 -3.1101:5:4 13.445:5:5
Matrix scaling M = scale*U'*U, scale = 1
Upper cholesky factor U (ignore lower nonzeros):
5 5
3.66633:1:1 -0.848699:1:2 -0.848699:1:3 -0.848699:1:4 -0.848487:1:5
0:2:1 3.56695:2:2 -1.07407:2:3 -1.07407:2:4 -1.07381:2:5
13.4434:3:1 0:3:2 3.4014:3:3 -1.46552:3:4 -1.46515:3:5
-3.11088:4:1 13.4434:4:2 0:4:3 3.06949:4:4 -2.32311:4:5
-3.11088:5:1 -3.11088:5:2 13.4434:5:3 0:5:4 2.0071:5:5
(6) 5.-1: "SetDBoundsStd"
dl(var_indep)_k =
5
-7.28846e-06:1 -1.76034e-06:2 -1.75996e-06:3 -1.75958e-06:4 -1.00001e-17:5
du(var_indep)_k =
5
1e+50:1 1e+50:2 1e+50:3 1e+50:4 1e+50:5
(6) 5: "TangentialStep"
qp_grad_k =
5
1.72853e-05:1 1.17572e-05:2 1.17568e-05:3 1.17565e-05:4 9.99687e-06:5
Determine if we can use simple bounds on pz ...
m = 3000
dynamic_cast<const MatrixIdentConcat*>(&Z_k) = 0xe2c76b0
||Ypy_k(var_indep)||inf = 3.1252363232e-09
Using simple bounds on pz ...
There are no finite bounds on dependent variables. There will be no extra inequality constraints added on D*pz ...
Calling QPKWIK to solve QP problem ...
||pz_k||inf = 2.5052443219e-06
nu_k.nz() = 4
max(|nu_k(i)|) = 3.4224117743e-05
||Zpz_k||2 = 3.9415350433e-06
pz_k =
5
-2.50524e-06:1 -1.75722e-06:2 -1.75684e-06:3 -1.75645e-06:4 3.12524e-09:5
nu_k(var_indep) =
5
0:1 -6.8492e-06:2 -6.85516e-06:3 -6.86113e-06:4 -3.42241e-05:5
Zpz(var_indep)_k =
5
-2.50524e-06:1 -1.75722e-06:2 -1.75684e-06:3 -1.75645e-06:4 3.12524e-09:5
(6) 6: "CalcDFromYPYZPZ"
(Ypy_k'*Zpz_k)/(||Ypy_k||2 * ||Zpz_k||2 + eps)
= (1.7579272235e-28)/(8.8328450816e-05 * 3.9415350433e-06 + 2.2250738585e-308)
= 5.0493431509e-19
||d_k||inf = 2.5083604808e-06
||d(var_dep)_k||inf = 1.6137749700e-06
||d(var_indep)_k||inf = 2.5083604808e-06
d(var_indep)_k =
5
-2.50836e-06:1 -1.76034e-06:2 -1.75996e-06:3 -1.75958e-06:4 -1.00001e-17:5
(6) 7: "CalcReducedGradLagrangian"
rGL_k =
5
1.72853e-05:1 4.90802e-06:2 4.90168e-06:3 4.89533e-06:4 -2.42272e-05:5
||rGL_k||inf = 2.4227242979e-05
rGL_k =
5
1.72853e-05:1 4.90802e-06:2 4.90168e-06:3 4.89533e-06:4 -2.42272e-05:5
(6) 8: "CheckConvergence"
scale_opt_factor = 1.0000000000e+00 (scale_opt_error_by = SCALE_BY_ONE)
scale_feas_factor = 1.0000000000e+00 (scale_feas_error_by = SCALE_BY_ONE)
scale_comp_factor = 1.0000000000e+00 (scale_comp_error_by = SCALE_BY_ONE)
opt_scale_factor = 1.0000172885e+00 (scale_opt_error_by_Gf = true)
opt_kkt_err_k = 2.4226824135e-05 < opt_tol = 1.0000000000e-02
feas_kkt_err_k = 1.6001110173e-03 > feas_tol = 1.0000000000e-07
comp_kkt_err_k = 1.2072668757e-11 < comp_tol = 1.0000000000e-06
step_err = 2.5083171159e-06 < step_tol = 1.0000000000e-02
Have not found the solution yet, have to keep going (k = 6) :-(
(6) 9.-1: "LineSearchFullStep"
f_k = 4.3078479209e-09
||c_k||inf = 1.6001110173e-03
alpha_k = 1.0000000000e+00
||x_kp1||inf = 1.4780094636e-05
f_kp1 = 3.0922559878e-10
||c_kp1||inf = 7.9473675342e-09
(6) 9: "LineSearch"
theta_k = ||c_k||1/c_k.dim() = 1.5716730031e-03
f_min==F_MIN_UNBOUNDED: Setting gamma_f_used = gamma_f = 1.0000000000e-05.
Beginning Filter line search method.
Current Filter
-----------------------------------------------------
| f_with_boundary | theta_with_boundary |
-----------------------------------------------------
| -1.1408882110e-08 1.5716572864e-03|
Iteration Status
----------------------------------------------------------------------------------------------------------
| alpha_k | f_kp1 | theta_kp1 | pt. status | comment |
----------------------------------------------------------------------------------------------------------
|1.0000000000e+00 3.0922559878e-10 4.8949810733e-09 accepted Fraction Reduction (! Switch Cond )|
Point was accepted - augmenting the filter ...
Augmenting the filter with the point:
f_with_boundary = f_kp1 - gamma_f_used*theta_kp1 = 3.0922559878e-10 - 1.0000000000e-05*4.8949810733e-09 = 3.0917664897e-10
theta_with_boundary = (1-gamma_theta)*theta_kp1 = (1-1.0000000000e-05)*4.8949810733e-09 = 4.8949321235e-09
(7) 1: "EvalNewPoint"
||x_k||inf = 1.4780094636e-05
||x(var_dep)_k||inf = 8.0843549147e-12
||x(var_indep)_k||inf = 1.4780094636e-05
x(var_indep)_k =
5
1.47801e-05:1 1e-05:2 1e-05:3 1e-05:4 1e-05:5
Updating the decomposition ...
Updating the range/null decompostion matrices ...
***********************************************************
*** DecompositionSystemVarReductImp::update_decomp(...) ***
************************************************************
Warning!!! mat_rel != MATRICES_INDEP_IMPS; The decompsition matrix objects may not be independent of each other!
****************************************************************
*** DecompositionSystemVarReductImp::get_basis_matrices(...) ***
****************************************************************
Allocated a new explicit matrix object for D = -inv(C)*N of type 'AbstractLinAlgPack::MultiVectorMutableDense' ...
End DecompositionSystemVarReductImp::get_basis_matrices(...)
Updating the basis matrix C and other matices using the BasisSystem object ...
Using a direct sparse solver to update basis ...
Using LAPACK xGETRF to refactor the basis matrix ...
End DecompositionSystemVarReductImp::update_decomp(...)
Printing the updated iteration quantities ...
f_k = 3.0922559878e-10
||Gf_k||inf = 1.4780094636e-05
||Gf_k(var_dep)_k||inf = 8.0843549147e-12
||Gf_k(var_indep)_k||inf = 1.4780094636e-05
||c_k||inf = 7.9473675342e-09
Gf(var_indep)_k =
5
1.47801e-05:1 1e-05:2 1e-05:3 1e-05:4 1e-05:5
(7) 2: "QuasiNormalStep"
||py|| = 8.0843549147e-12
||Ypy||2 = 3.1177993328e-10
(7) 2.1: "CheckDecompositionFromPy"
beta = ||py||/||c|| = 1.0172368246e-03
(7) 2.2: "CheckDecompositionFromRPy"
beta = ||R*py_k + c_k(decomp)||inf / (||c_k(decomp)||inf + small_number)
= 6.6174449004e-24 / (7.9473675342e-09 + 2.2250738585e-308)
= 8.3265872278e-16
(7) 3: "ReducedGradient"
||rGf||inf = 1.4780094636e-05
rGf_k =
5
1.47801e-05:1 1e-05:2 1e-05:3 1e-05:4 1e-05:5
(7) 4.-1: "CheckSkipBFGSUpdate"
ratio = (skip_bfgs_prop_const/sqrt(||rGL_km1||+||c_km1||))*(||Zpz_km1||/||Ypy_km1||)
= (1.0000000000e+01/sqrt(3.0948692946e-05+8.6084094835e-02))
* (3.9415350433e-06/8.8328450816e-05)
= 1.5206359932e+00
ratio > 1
Perform BFGS update if you can ...
(7) 4: "ReducedHessian"
Performing Secant update ...
||y_bfgs||inf = 2.5052443219e-06
||s_bfgs||inf = 2.5052443219e-06
y_bfgs =
5
-2.50524e-06:1 -1.75722e-06:2 -1.75684e-06:3 -1.75645e-06:4 3.12524e-09:5
s_bfgs =
5
-2.50524e-06:1 -1.75722e-06:2 -1.75684e-06:3 -1.75645e-06:4 3.12524e-09:5
Considering the dampened update ...
s_bfgs'*y_bfgs = 1.5535698401e-11 >= s_bfgs' * B * s_bfgs = 6.9214067476e-11
Perform the undamped update ...
B after the BFGS update =
Unfactored symmetric matrix stored as lower triangle (ignore upper nonzeros):
5 5
9.52915:1:1 0:1:2 3.56695:1:3 -1.07407:1:4 -1.07407:1:5
-4.05396:2:1 13.2941:2:2 0:2:3 3.4014:2:4 -1.46552:2:5
-4.05244:3:1 -3.25975:3:2 13.295:3:3 0:3:4 3.06949:3:5
-4.05091:4:1 -3.25934:4:2 -3.25893:4:3 13.2958:4:4 0:4:5
2.93911:5:1 -1.39248:5:2 -1.3947:5:3 -1.39693:5:4 4.96462:5:5
||rHL_k||inf = 2.4625571263e+01
cond_inf(rHL_k) = 3.1556895452e+01
rHL_k =
Unfactored symmetric matrix stored as lower triangle (ignore upper nonzeros):
5 5
9.52915:1:1 0:1:2 3.40139:1:3 -1.46521:1:4 -1.4649:1:5
-4.05396:2:1 13.2941:2:2 0:2:3 3.06997:2:4 -2.32186:2:5
-4.05244:3:1 -3.25975:3:2 13.295:3:3 0:3:4 2.00916:3:5
-4.05091:4:1 -3.25934:4:2 -3.25893:4:3 13.2958:4:4 0:4:5
2.93911:5:1 -1.39248:5:2 -1.3947:5:3 -1.39693:5:4 4.96462:5:5
Matrix scaling M = scale*U'*U, scale = 1
Upper cholesky factor U (ignore lower nonzeros):
5 5
3.08693:1:1 -1.31326:1:2 -1.31277:1:3 -1.31228:1:4 0.952114:1:5
0:2:1 3.40139:2:2 -1.46521:2:3 -1.4649:2:4 -0.0417781:2:5
13.2941:3:1 0:3:2 3.06997:3:3 -2.32186:3:4 -0.0671046:3:5
-3.25975:4:1 13.295:4:2 0:4:3 2.00916:4:4 -0.181417:4:5
-3.25934:5:1 -3.25893:5:2 13.2958:5:3 0:5:4 2.00473:5:5
(7) 5.-1: "SetDBoundsStd"
dl(var_indep)_k =
5
-4.78009e-06:1 0:2 0:3 0:4 0:5
du(var_indep)_k =
5
1e+50:1 1e+50:2 1e+50:3 1e+50:4 1e+50:5
(7) 5: "TangentialStep"
qp_grad_k =
5
1.47801e-05:1 1e-05:2 1e-05:3 1e-05:4 1e-05:5
Determine if we can use simple bounds on pz ...
m = 3000
dynamic_cast<const MatrixIdentConcat*>(&Z_k) = 0xe2c76b0
||Ypy_k(var_indep)||inf = 7.8420208892e-20
Using simple bounds on pz ...
There are no finite bounds on dependent variables. There will be no extra inequality constraints added on D*pz ...
Calling QPKWIK to solve QP problem ...
||pz_k||inf = 1.5510400571e-06
nu_k.nz() = 4
max(|nu_k(i)|) = 1.6287853297e-05
||Zpz_k||2 = 1.5510400571e-06
pz_k =
5
-1.55104e-06:1 3.86837e-20:2 3.86646e-20:3 3.86426e-20:4 4.74479e-35:5
nu_k(var_indep) =
5
0:1 -1.62879e-05:2 -1.62855e-05:3 -1.62831e-05:4 -5.44132e-06:5
Zpz(var_indep)_k =
5
-1.55104e-06:1 3.86837e-20:2 3.86646e-20:3 3.86426e-20:4 4.74479e-35:5
(7) 6: "CalcDFromYPYZPZ"
(Ypy_k'*Zpz_k)/(||Ypy_k||2 * ||Zpz_k||2 + eps)
= (-3.6810718738e-39)/(3.1177993328e-10 * 1.5510400571e-06 + 2.2250738585e-308)
= -7.6120761359e-24
||d_k||inf = 1.5510400571e-06
||d(var_dep)_k||inf = 8.0843298368e-12
||d(var_indep)_k||inf = 1.5510400571e-06
d(var_indep)_k =
5
-1.55104e-06:1 0:2 0:3 0:4 0:5
(7) 7: "CalcReducedGradLagrangian"
rGL_k =
5
1.47801e-05:1 -6.28785e-06:2 -6.28549e-06:3 -6.28313e-06:4 4.55868e-06:5
||rGL_k||inf = 1.4780094636e-05
rGL_k =
5
1.47801e-05:1 -6.28785e-06:2 -6.28549e-06:3 -6.28313e-06:4 4.55868e-06:5
(7) 8: "CheckConvergence"
scale_opt_factor = 1.0000000000e+00 (scale_opt_error_by = SCALE_BY_ONE)
scale_feas_factor = 1.0000000000e+00 (scale_feas_error_by = SCALE_BY_ONE)
scale_comp_factor = 1.0000000000e+00 (scale_comp_error_by = SCALE_BY_ONE)
opt_scale_factor = 1.0000147801e+00 (scale_opt_error_by_Gf = true)
opt_kkt_err_k = 1.4779876188e-05 < opt_tol = 1.0000000000e-02
feas_kkt_err_k = 7.9473675342e-09 < feas_tol = 1.0000000000e-07
comp_kkt_err_k = 0.0000000000e+00 < comp_tol = 1.0000000000e-06
step_err = 1.5510171329e-06 < step_tol = 1.0000000000e-02
Jackpot! Found the solution!!!!!! (k = 7)
1.8.6