ROL
|
Provides the interface to evaluate the augmented Lagrangian. More...
#include <ROL_AugmentedLagrangian.hpp>
Public Member Functions | |
AugmentedLagrangian (const ROL::Ptr< Objective< Real > > &obj, const ROL::Ptr< Constraint< Real > > &con, const Vector< Real > &multiplier, const Real penaltyParameter, const Vector< Real > &optVec, const Vector< Real > &conVec, ROL::ParameterList &parlist) | |
Constructor. More... | |
AugmentedLagrangian (const ROL::Ptr< Objective< Real > > &obj, const ROL::Ptr< Constraint< Real > > &con, const Vector< Real > &multiplier, const Real penaltyParameter, const Vector< Real > &optVec, const Vector< Real > &conVec, const bool scaleLagrangian, const int HessianApprox) | |
Constructor. More... | |
AugmentedLagrangian () | |
Null constructor. More... | |
virtual void | update (const Vector< Real > &x, bool flag=true, int iter=-1) |
Update objective function. More... | |
void | setScaling (const Real fscale, const Real cscale=1.0) |
virtual Real | value (const Vector< Real > &x, Real &tol) |
Compute value. More... | |
virtual void | gradient (Vector< Real > &g, const Vector< Real > &x, Real &tol) |
Compute gradient. More... | |
virtual void | hessVec (Vector< Real > &hv, const Vector< Real > &v, const Vector< Real > &x, Real &tol) |
Apply Hessian approximation to vector. More... | |
virtual Real | getObjectiveValue (const Vector< Real > &x) |
const Ptr< const Vector< Real > > | getObjectiveGradient (const Vector< Real > &x) |
virtual void | getConstraintVec (Vector< Real > &c, const Vector< Real > &x) |
virtual int | getNumberConstraintEvaluations (void) const |
virtual int | getNumberFunctionEvaluations (void) const |
virtual int | getNumberGradientEvaluations (void) const |
virtual void | reset (const Vector< Real > &multiplier, const Real penaltyParameter) |
Public Member Functions inherited from ROL::Objective< Real > | |
virtual | ~Objective () |
Objective () | |
virtual void | update (const Vector< Real > &x, UpdateType type, int iter=-1) |
Update objective function. More... | |
virtual Real | dirDeriv (const Vector< Real > &x, const Vector< Real > &d, Real &tol) |
Compute directional derivative. More... | |
virtual void | invHessVec (Vector< Real > &hv, const Vector< Real > &v, const Vector< Real > &x, Real &tol) |
Apply inverse Hessian approximation to vector. More... | |
virtual void | precond (Vector< Real > &Pv, const Vector< Real > &v, const Vector< Real > &x, Real &tol) |
Apply preconditioner to vector. More... | |
virtual void | prox (Vector< Real > &Pv, const Vector< Real > &v, Real t, Real &tol) |
virtual std::vector < std::vector< Real > > | checkGradient (const Vector< Real > &x, const Vector< Real > &d, const bool printToStream=true, std::ostream &outStream=std::cout, const int numSteps=ROL_NUM_CHECKDERIV_STEPS, const int order=1) |
Finite-difference gradient check. More... | |
virtual std::vector < std::vector< Real > > | checkGradient (const Vector< Real > &x, const Vector< Real > &g, const Vector< Real > &d, const bool printToStream=true, std::ostream &outStream=std::cout, const int numSteps=ROL_NUM_CHECKDERIV_STEPS, const int order=1) |
Finite-difference gradient check. More... | |
virtual std::vector < std::vector< Real > > | checkGradient (const Vector< Real > &x, const Vector< Real > &d, const std::vector< Real > &steps, const bool printToStream=true, std::ostream &outStream=std::cout, const int order=1) |
Finite-difference gradient check with specified step sizes. More... | |
virtual std::vector < std::vector< Real > > | checkGradient (const Vector< Real > &x, const Vector< Real > &g, const Vector< Real > &d, const std::vector< Real > &steps, const bool printToStream=true, std::ostream &outStream=std::cout, const int order=1) |
Finite-difference gradient check with specified step sizes. More... | |
virtual std::vector < std::vector< Real > > | checkHessVec (const Vector< Real > &x, const Vector< Real > &v, const bool printToStream=true, std::ostream &outStream=std::cout, const int numSteps=ROL_NUM_CHECKDERIV_STEPS, const int order=1) |
Finite-difference Hessian-applied-to-vector check. More... | |
virtual std::vector < std::vector< Real > > | checkHessVec (const Vector< Real > &x, const Vector< Real > &hv, const Vector< Real > &v, const bool printToStream=true, std::ostream &outStream=std::cout, const int numSteps=ROL_NUM_CHECKDERIV_STEPS, const int order=1) |
Finite-difference Hessian-applied-to-vector check. More... | |
virtual std::vector < std::vector< Real > > | checkHessVec (const Vector< Real > &x, const Vector< Real > &v, const std::vector< Real > &steps, const bool printToStream=true, std::ostream &outStream=std::cout, const int order=1) |
Finite-difference Hessian-applied-to-vector check with specified step sizes. More... | |
virtual std::vector < std::vector< Real > > | checkHessVec (const Vector< Real > &x, const Vector< Real > &hv, const Vector< Real > &v, const std::vector< Real > &steps, const bool printToStream=true, std::ostream &outStream=std::cout, const int order=1) |
Finite-difference Hessian-applied-to-vector check with specified step sizes. More... | |
virtual std::vector< Real > | checkHessSym (const Vector< Real > &x, const Vector< Real > &v, const Vector< Real > &w, const bool printToStream=true, std::ostream &outStream=std::cout) |
Hessian symmetry check. More... | |
virtual std::vector< Real > | checkHessSym (const Vector< Real > &x, const Vector< Real > &hv, const Vector< Real > &v, const Vector< Real > &w, const bool printToStream=true, std::ostream &outStream=std::cout) |
Hessian symmetry check. More... | |
virtual void | setParameter (const std::vector< Real > ¶m) |
Private Attributes | |
const ROL::Ptr< Objective< Real > > | obj_ |
ROL::Ptr< QuadraticPenalty < Real > > | pen_ |
Real | penaltyParameter_ |
ROL::Ptr< Vector< Real > > | dualOptVector_ |
Real | fval_ |
ROL::Ptr< Vector< Real > > | gradient_ |
Real | fscale_ |
int | nfval_ |
int | ngval_ |
bool | scaleLagrangian_ |
bool | isValueComputed_ |
bool | isGradientComputed_ |
Additional Inherited Members | |
Protected Member Functions inherited from ROL::Objective< Real > | |
const std::vector< Real > | getParameter (void) const |
Provides the interface to evaluate the augmented Lagrangian.
This class implements the augmented Lagrangian functional for use with ROL::AugmentedLagrangianStep. Given a function \(f:\mathcal{X}\to\mathbb{R}\) and an equality constraint \(c:\mathcal{X}\to\mathcal{C}\), the augmented Lagrangian functional is
\[ L_A(x,\lambda,\mu) = f(x) + \langle \lambda, c(x)\rangle_{\mathcal{C}^*,\mathcal{C}} + \frac{\mu}{2} \langle \mathfrak{R}c(x),c(x)\rangle_{\mathcal{C}^*,\mathcal{C}} \]
where \(\lambda\in\mathcal{C}^*\) denotes the Lagrange multiplier estimate, \(\mu > 0\) is the penalty parameter and \(\mathfrak{R}\in\mathcal{L}(\mathcal{C},\mathcal{C}^*)\) is the Riesz operator on the constraint space.
This implementation permits the scaling of \(L_A\) by \(\mu^{-1}\) and also permits the Hessian approximation
\[ \nabla^2_x L_A(x,\lambda,\mu)v \approx \nabla^2 f(x) v + \mu c'(x)^*\mathfrak{R} c'(x)v. \]
Definition at line 52 of file ROL_AugmentedLagrangian.hpp.
|
inline |
Constructor.
This creates a valid AugmentedLagrangian object.
[in] | obj | is an objective function. |
[in] | con | is an equality constraint. |
[in] | mulitplier | is a Lagrange multiplier vector. |
[in] | penaltyParameter | is the penalty parameter. |
[in] | optVec | is an optimization space vector. |
[in] | conVec | is a constraint space vector. |
[in] | parlist | is a parameter list. |
Definition at line 92 of file ROL_AugmentedLagrangian.hpp.
References ROL::Vector< Real >::dual(), ROL::AugmentedLagrangian< Real >::dualOptVector_, ROL::AugmentedLagrangian< Real >::gradient_, ROL::AugmentedLagrangian< Real >::pen_, and ROL::AugmentedLagrangian< Real >::scaleLagrangian_.
|
inline |
Constructor.
This creates a valid AugmentedLagrangian object.
[in] | obj | is an objective function. |
[in] | con | is an equality constraint. |
[in] | mulitplier | is a Lagrange multiplier vector. |
[in] | penaltyParameter | is the penalty parameter. |
[in] | optVec | is an optimization space vector. |
[in] | conVec | is a constraint space vector. |
[in] | parlist | is a parameter list. |
Definition at line 125 of file ROL_AugmentedLagrangian.hpp.
References ROL::Vector< Real >::dual(), ROL::AugmentedLagrangian< Real >::dualOptVector_, ROL::AugmentedLagrangian< Real >::gradient_, ROL::AugmentedLagrangian< Real >::pen_, and ROL::AugmentedLagrangian< Real >::scaleLagrangian_.
|
inline |
Null constructor.
This constructor is only used for inheritance and does not create a valid AugmentedLagrangian object. Do not use.
Definition at line 150 of file ROL_AugmentedLagrangian.hpp.
|
inlinevirtual |
Update objective function.
This function updates the objective function at new iterations.
[in] | x | is the new iterate. |
[in] | flag | is true if the iterate has changed. |
[in] | iter | is the outer algorithm iterations count. |
Reimplemented from ROL::Objective< Real >.
Reimplemented in ROL::Reduced_AugmentedLagrangian_SimOpt< Real >.
Definition at line 156 of file ROL_AugmentedLagrangian.hpp.
References ROL::AugmentedLagrangian< Real >::isGradientComputed_, ROL::AugmentedLagrangian< Real >::isValueComputed_, ROL::AugmentedLagrangian< Real >::obj_, and ROL::AugmentedLagrangian< Real >::pen_.
Referenced by ROL::AugmentedLagrangianStep< Real >::initialize(), and ROL::AugmentedLagrangianStep< Real >::update().
|
inline |
Definition at line 163 of file ROL_AugmentedLagrangian.hpp.
References ROL::AugmentedLagrangian< Real >::fscale_, and ROL::AugmentedLagrangian< Real >::pen_.
Referenced by ROL::AugmentedLagrangianStep< Real >::initialize().
|
inlinevirtual |
Compute value.
This function returns the objective function value.
[in] | x | is the current iterate. |
[in] | tol | is a tolerance for inexact objective function computation. |
Implements ROL::Objective< Real >.
Reimplemented in ROL::Reduced_AugmentedLagrangian_SimOpt< Real >.
Definition at line 168 of file ROL_AugmentedLagrangian.hpp.
References ROL::AugmentedLagrangian< Real >::fscale_, ROL::AugmentedLagrangian< Real >::fval_, ROL::AugmentedLagrangian< Real >::isValueComputed_, ROL::AugmentedLagrangian< Real >::nfval_, ROL::AugmentedLagrangian< Real >::obj_, ROL::AugmentedLagrangian< Real >::pen_, ROL::AugmentedLagrangian< Real >::penaltyParameter_, and ROL::AugmentedLagrangian< Real >::scaleLagrangian_.
|
inlinevirtual |
Compute gradient.
This function returns the objective function gradient.
[out] | g | is the gradient. |
[in] | x | is the current iterate. |
[in] | tol | is a tolerance for inexact objective function computation. |
The default implementation is a finite-difference approximation based on the function value. This requires the definition of a basis \(\{\phi_i\}\) for the optimization vectors x and the definition of a basis \(\{\psi_j\}\) for the dual optimization vectors (gradient vectors g). The bases must be related through the Riesz map, i.e., \( R \{\phi_i\} = \{\psi_j\}\), and this must be reflected in the implementation of the ROL::Vector::dual() method.
Reimplemented from ROL::Objective< Real >.
Reimplemented in ROL::Reduced_AugmentedLagrangian_SimOpt< Real >.
Definition at line 184 of file ROL_AugmentedLagrangian.hpp.
References ROL::AugmentedLagrangian< Real >::dualOptVector_, ROL::AugmentedLagrangian< Real >::fscale_, ROL::AugmentedLagrangian< Real >::gradient_, ROL::AugmentedLagrangian< Real >::isGradientComputed_, ROL::AugmentedLagrangian< Real >::ngval_, ROL::AugmentedLagrangian< Real >::obj_, ROL::AugmentedLagrangian< Real >::pen_, ROL::AugmentedLagrangian< Real >::penaltyParameter_, ROL::Vector< Real >::plus(), ROL::Vector< Real >::scale(), ROL::AugmentedLagrangian< Real >::scaleLagrangian_, and ROL::Vector< Real >::set().
Referenced by ROL::AugmentedLagrangianStep< Real >::computeGradient().
|
inlinevirtual |
Apply Hessian approximation to vector.
This function applies the Hessian of the objective function to the vector \(v\).
[out] | hv | is the the action of the Hessian on \(v\). |
[in] | v | is the direction vector. |
[in] | x | is the current iterate. |
[in] | tol | is a tolerance for inexact objective function computation. |
Reimplemented from ROL::Objective< Real >.
Reimplemented in ROL::Reduced_AugmentedLagrangian_SimOpt< Real >.
Definition at line 201 of file ROL_AugmentedLagrangian.hpp.
References ROL::AugmentedLagrangian< Real >::dualOptVector_, ROL::AugmentedLagrangian< Real >::fscale_, ROL::AugmentedLagrangian< Real >::obj_, ROL::AugmentedLagrangian< Real >::pen_, ROL::AugmentedLagrangian< Real >::penaltyParameter_, ROL::Vector< Real >::plus(), ROL::Vector< Real >::scale(), and ROL::AugmentedLagrangian< Real >::scaleLagrangian_.
|
inlinevirtual |
Reimplemented in ROL::Reduced_AugmentedLagrangian_SimOpt< Real >.
Definition at line 215 of file ROL_AugmentedLagrangian.hpp.
References ROL::AugmentedLagrangian< Real >::fval_, ROL::AugmentedLagrangian< Real >::isValueComputed_, ROL::AugmentedLagrangian< Real >::nfval_, and ROL::AugmentedLagrangian< Real >::obj_.
Referenced by ROL::AugmentedLagrangianStep< Real >::initialize(), and ROL::AugmentedLagrangianStep< Real >::update().
|
inline |
Definition at line 225 of file ROL_AugmentedLagrangian.hpp.
References ROL::AugmentedLagrangian< Real >::gradient_, ROL::AugmentedLagrangian< Real >::isGradientComputed_, ROL::AugmentedLagrangian< Real >::ngval_, and ROL::AugmentedLagrangian< Real >::obj_.
Referenced by ROL::AugmentedLagrangianStep< Real >::initialize().
|
inlinevirtual |
Reimplemented in ROL::Reduced_AugmentedLagrangian_SimOpt< Real >.
Definition at line 236 of file ROL_AugmentedLagrangian.hpp.
References ROL::AugmentedLagrangian< Real >::pen_.
Referenced by ROL::AugmentedLagrangianStep< Real >::initialize(), and ROL::AugmentedLagrangianStep< Real >::update().
|
inlinevirtual |
Reimplemented in ROL::Reduced_AugmentedLagrangian_SimOpt< Real >.
Definition at line 241 of file ROL_AugmentedLagrangian.hpp.
References ROL::AugmentedLagrangian< Real >::pen_.
Referenced by ROL::AugmentedLagrangianStep< Real >::initialize(), and ROL::AugmentedLagrangianStep< Real >::update().
|
inlinevirtual |
Reimplemented in ROL::Reduced_AugmentedLagrangian_SimOpt< Real >.
Definition at line 246 of file ROL_AugmentedLagrangian.hpp.
References ROL::AugmentedLagrangian< Real >::nfval_.
Referenced by ROL::AugmentedLagrangianStep< Real >::initialize(), and ROL::AugmentedLagrangianStep< Real >::update().
|
inlinevirtual |
Reimplemented in ROL::Reduced_AugmentedLagrangian_SimOpt< Real >.
Definition at line 251 of file ROL_AugmentedLagrangian.hpp.
References ROL::AugmentedLagrangian< Real >::ngval_.
Referenced by ROL::AugmentedLagrangianStep< Real >::initialize(), and ROL::AugmentedLagrangianStep< Real >::update().
|
inlinevirtual |
Reimplemented in ROL::Reduced_AugmentedLagrangian_SimOpt< Real >.
Definition at line 256 of file ROL_AugmentedLagrangian.hpp.
References ROL::AugmentedLagrangian< Real >::nfval_, ROL::AugmentedLagrangian< Real >::ngval_, and ROL::AugmentedLagrangian< Real >::pen_.
Referenced by ROL::AugmentedLagrangianStep< Real >::update().
|
private |
Definition at line 55 of file ROL_AugmentedLagrangian.hpp.
Referenced by ROL::AugmentedLagrangian< Real >::getObjectiveGradient(), ROL::AugmentedLagrangian< Real >::getObjectiveValue(), ROL::AugmentedLagrangian< Real >::gradient(), ROL::AugmentedLagrangian< Real >::hessVec(), ROL::AugmentedLagrangian< Real >::update(), and ROL::AugmentedLagrangian< Real >::value().
|
private |
Definition at line 56 of file ROL_AugmentedLagrangian.hpp.
Referenced by ROL::AugmentedLagrangian< Real >::AugmentedLagrangian(), ROL::AugmentedLagrangian< Real >::getConstraintVec(), ROL::AugmentedLagrangian< Real >::getNumberConstraintEvaluations(), ROL::AugmentedLagrangian< Real >::gradient(), ROL::AugmentedLagrangian< Real >::hessVec(), ROL::AugmentedLagrangian< Real >::reset(), ROL::AugmentedLagrangian< Real >::setScaling(), ROL::AugmentedLagrangian< Real >::update(), and ROL::AugmentedLagrangian< Real >::value().
|
private |
Definition at line 57 of file ROL_AugmentedLagrangian.hpp.
Referenced by ROL::AugmentedLagrangian< Real >::gradient(), ROL::AugmentedLagrangian< Real >::hessVec(), and ROL::AugmentedLagrangian< Real >::value().
|
private |
Definition at line 60 of file ROL_AugmentedLagrangian.hpp.
Referenced by ROL::AugmentedLagrangian< Real >::AugmentedLagrangian(), ROL::AugmentedLagrangian< Real >::gradient(), and ROL::AugmentedLagrangian< Real >::hessVec().
|
private |
Definition at line 63 of file ROL_AugmentedLagrangian.hpp.
Referenced by ROL::AugmentedLagrangian< Real >::getObjectiveValue(), and ROL::AugmentedLagrangian< Real >::value().
|
private |
Definition at line 64 of file ROL_AugmentedLagrangian.hpp.
Referenced by ROL::AugmentedLagrangian< Real >::AugmentedLagrangian(), ROL::AugmentedLagrangian< Real >::getObjectiveGradient(), and ROL::AugmentedLagrangian< Real >::gradient().
|
private |
Definition at line 67 of file ROL_AugmentedLagrangian.hpp.
Referenced by ROL::AugmentedLagrangian< Real >::gradient(), ROL::AugmentedLagrangian< Real >::hessVec(), ROL::AugmentedLagrangian< Real >::setScaling(), and ROL::AugmentedLagrangian< Real >::value().
|
private |
|
private |
|
private |
Definition at line 74 of file ROL_AugmentedLagrangian.hpp.
Referenced by ROL::AugmentedLagrangian< Real >::AugmentedLagrangian(), ROL::AugmentedLagrangian< Real >::gradient(), ROL::AugmentedLagrangian< Real >::hessVec(), and ROL::AugmentedLagrangian< Real >::value().
|
private |
Definition at line 77 of file ROL_AugmentedLagrangian.hpp.
Referenced by ROL::AugmentedLagrangian< Real >::getObjectiveValue(), ROL::AugmentedLagrangian< Real >::update(), and ROL::AugmentedLagrangian< Real >::value().
|
private |
Definition at line 78 of file ROL_AugmentedLagrangian.hpp.
Referenced by ROL::AugmentedLagrangian< Real >::getObjectiveGradient(), ROL::AugmentedLagrangian< Real >::gradient(), and ROL::AugmentedLagrangian< Real >::update().