44 #ifndef ROL_TYPEP_SPECTRALGRADIENTALGORITHM_DEF_HPP
45 #define ROL_TYPEP_SPECTRALGRADIENTALGORITHM_DEF_HPP
50 template<
typename Real>
57 ParameterList &lslist = list.sublist(
"Step").sublist(
"Spectral Gradient");
58 maxit_ = lslist.get(
"Function Evaluation Limit", 20);
59 lambda_ = lslist.get(
"Initial Spectral Step Size", -1.0);
60 lambdaMin_ = lslist.get(
"Minimum Spectral Step Size", 1e-8);
61 lambdaMax_ = lslist.get(
"Maximum Spectral Step Size", 1e8);
62 sigma1_ = lslist.get(
"Lower Step Size Safeguard", 0.1);
63 sigma2_ = lslist.get(
"Upper Step Size Safeguard", 0.9);
64 rhodec_ = lslist.get(
"Backtracking Rate", 1e-1);
65 gamma_ = lslist.get(
"Sufficient Decrease Tolerance", 1e-4);
66 maxSize_ = lslist.get(
"Maximum Storage Size", 10);
67 initProx_ = lslist.get(
"Apply Prox to Initial Guess",
false);
68 t0_ = list.sublist(
"Status Test").get(
"Gradient Scale" , 1.0);
69 verbosity_ = list.sublist(
"General").get(
"Output Level", 0);
70 writeHeader_ = verbosity_ > 2;
73 template<
typename Real>
80 std::ostream &outStream) {
82 Real ftol = std::sqrt(ROL_EPSILON<Real>());
87 nobj.
prox(*state_->iterateVec,x,t0_,ftol); state_->nprox++;
88 x.
set(*state_->iterateVec);
91 state_->svalue = sobj.
value(x,ftol); state_->nsval++;
93 state_->nvalue = nobj.
value(x,ftol); state_->nnval++;
94 state_->value = state_->svalue + state_->nvalue;
95 sobj.
gradient(*state_->gradientVec,x,ftol); state_->ngrad++;
96 dg.
set(state_->gradientVec->dual());
97 if (lambda_ <= zero && state_->gnorm != zero)
98 lambda_ = std::max(lambdaMin_,std::min(t0_,lambdaMax_));
99 pgstep(*state_->iterateVec, *state_->stepVec, nobj, x, dg, lambda_, ftol);
100 state_->snorm = state_->stepVec->norm();
101 state_->gnorm = state_->snorm / lambda_;
104 template<
typename Real>
109 std::ostream &outStream ) {
110 const Real half(0.5), one(1), eps(std::sqrt(ROL_EPSILON<Real>()));
113 initialize(x,g,sobj,nobj,*s,*dg,outStream);
114 Real strial(0), ntrial(0), Ftrial(0), Fmin(0), Fmax(0), Qk(0), alpha(1), rhoTmp(1);
115 Real gs(0), ys(0), snorm(state_->snorm), ss(0), tol(std::sqrt(ROL_EPSILON<Real>()));
117 std::deque<Real> Fqueue; Fqueue.push_back(state_->value);
119 Fmin = state_->value;
123 if (verbosity_ > 0) writeOutput(outStream,
true);
126 while (status_->check(*state_)) {
130 strial = sobj.
value(*state_->iterateVec,tol);
132 ntrial = nobj.
value(*state_->iterateVec,tol);
133 Ftrial = strial + ntrial;
136 Fmax = *std::max_element(Fqueue.begin(),Fqueue.end());
137 gs = state_->gradientVec->apply(*state_->stepVec);
138 Qk = gs + ntrial - state_->nvalue;
139 if (verbosity_ > 1) {
140 outStream <<
" In TypeP::SpectralGradientAlgorithm Line Search" << std::endl;
141 outStream <<
" Step size: " << alpha << std::endl;
142 outStream <<
" Trial objective value: " << Ftrial << std::endl;
143 outStream <<
" Max stored objective value: " << Fmax << std::endl;
144 outStream <<
" Computed reduction: " << Fmax-Ftrial << std::endl;
145 outStream <<
" Dot product of gradient and step: " << Qk << std::endl;
146 outStream <<
" Sufficient decrease bound: " << -Qk*gamma_ << std::endl;
147 outStream <<
" Number of function evaluations: " << ls_nfval << std::endl;
149 while (Ftrial > Fmax + gamma_*Qk && ls_nfval < maxit_) {
151 rhoTmp = std::min(one,-half*Qk/(strial-state_->svalue-alpha*gs));
153 alpha = ((sigma1_ <= rhoTmp && rhoTmp <= sigma2_) ? rhoTmp : rhodec_)*alpha;
155 state_->iterateVec->set(x);
156 state_->iterateVec->axpy(alpha,*state_->stepVec);
159 strial = sobj.
value(*state_->iterateVec,tol);
161 ntrial = nobj.
value(*state_->iterateVec,tol);
162 Ftrial = strial + ntrial;
164 Qk = alpha * gs + ntrial - state_->nvalue;
165 if (verbosity_ > 1) {
166 outStream <<
" In TypeP::SpectralGradientAlgorithm: Line Search" << std::endl;
167 outStream <<
" Step size: " << alpha << std::endl;
168 outStream <<
" Trial objective value: " << Ftrial << std::endl;
169 outStream <<
" Max stored objective value: " << Fmax << std::endl;
170 outStream <<
" Computed reduction: " << Fmax-Ftrial << std::endl;
171 outStream <<
" Dot product of gradient and step: " << Qk << std::endl;
172 outStream <<
" Sufficient decrease bound: " << -Qk*gamma_ << std::endl;
173 outStream <<
" Number of function evaluations: " << ls_nfval << std::endl;
176 state_->nsval += ls_nfval;
177 state_->nnval += ls_nfval;
178 if (static_cast<int>(Fqueue.size()) == maxSize_) Fqueue.pop_front();
179 Fqueue.push_back(Ftrial);
183 state_->value = Ftrial;
184 state_->svalue = strial;
185 state_->nvalue = ntrial;
186 state_->searchSize = alpha;
187 state_->snorm = alpha * snorm;
188 state_->stepVec->scale(alpha);
189 x.
set(*state_->iterateVec);
194 if (state_->value <= Fmin) {
195 Fmin = state_->value;
200 y->set(*state_->gradientVec);
202 sobj.
gradient(*state_->gradientVec,x,tol); state_->ngrad++;
203 dg->set(state_->gradientVec->dual());
204 y->plus(*state_->gradientVec);
205 ys = y->apply(*state_->stepVec);
206 ss = state_->snorm * state_->snorm;
207 lambda_ = (ys<=eps*state_->snorm ? lambdaMax_ : std::max(lambdaMin_,std::min(ss/ys,lambdaMax_)));
210 pgstep(*state_->iterateVec, *state_->stepVec, nobj, x, *dg, lambda_, tol);
211 snorm = state_->stepVec->norm();
212 state_->gnorm = snorm / lambda_;
215 if (verbosity_ > 0) writeOutput(outStream,writeHeader_);
218 state_->value = Fmin;
222 template<
typename Real>
224 std::ios_base::fmtflags osFlags(os.flags());
225 if (verbosity_ > 1) {
226 os << std::string(109,
'-') << std::endl;
227 os <<
"Spectral proximal gradient with nonmonotone line search";
228 os <<
" status output definitions" << std::endl << std::endl;
229 os <<
" iter - Number of iterates (steps taken)" << std::endl;
230 os <<
" value - Objective function value" << std::endl;
231 os <<
" gnorm - Norm of the proximal gradient with parameter lambda" << std::endl;
232 os <<
" snorm - Norm of the step (update to optimization vector)" << std::endl;
233 os <<
" alpha - Line search step length" << std::endl;
234 os <<
" lambda - Spectral step length" << std::endl;
235 os <<
" #sval - Cumulative number of times the smooth objective function was evaluated" << std::endl;
236 os <<
" #nval - Cumulative number of times the nonsmooth objective function was evaluated" << std::endl;
237 os <<
" #grad - Cumulative number of times the gradient was computed" << std::endl;
238 os <<
" #prox - Cumulative number of times the proximal operator was computed" << std::endl;
239 os << std::string(109,
'-') << std::endl;
243 os << std::setw(6) << std::left <<
"iter";
244 os << std::setw(15) << std::left <<
"value";
245 os << std::setw(15) << std::left <<
"gnorm";
246 os << std::setw(15) << std::left <<
"snorm";
247 os << std::setw(15) << std::left <<
"alpha";
248 os << std::setw(15) << std::left <<
"lambda";
249 os << std::setw(10) << std::left <<
"#sval";
250 os << std::setw(10) << std::left <<
"#nval";
251 os << std::setw(10) << std::left <<
"#grad";
252 os << std::setw(10) << std::left <<
"#nprox";
257 template<
typename Real>
259 std::ios_base::fmtflags osFlags(os.flags());
260 os << std::endl <<
"Spectral Proximal Gradient with Nonmonotone Line Search (Type P)" << std::endl;
264 template<
typename Real>
266 std::ios_base::fmtflags osFlags(os.flags());
267 os << std::scientific << std::setprecision(6);
268 if ( state_->iter == 0 ) writeName(os);
269 if ( write_header ) writeHeader(os);
270 if ( state_->iter == 0 ) {
272 os << std::setw(6) << std::left << state_->iter;
273 os << std::setw(15) << std::left << state_->value;
274 os << std::setw(15) << std::left << state_->gnorm;
275 os << std::setw(15) << std::left <<
"---";
276 os << std::setw(15) << std::left <<
"---";
277 os << std::setw(15) << std::left << lambda_;
278 os << std::setw(10) << std::left << state_->nsval;
279 os << std::setw(10) << std::left << state_->nnval;
280 os << std::setw(10) << std::left << state_->ngrad;
281 os << std::setw(10) << std::left << state_->nprox;
286 os << std::setw(6) << std::left << state_->iter;
287 os << std::setw(15) << std::left << state_->value;
288 os << std::setw(15) << std::left << state_->gnorm;
289 os << std::setw(15) << std::left << state_->snorm;
290 os << std::setw(15) << std::left << state_->searchSize;
291 os << std::setw(15) << std::left << lambda_;
292 os << std::setw(10) << std::left << state_->nsval;
293 os << std::setw(10) << std::left << state_->nnval;
294 os << std::setw(10) << std::left << state_->ngrad;
295 os << std::setw(10) << std::left << state_->nprox;
Provides the interface to evaluate objective functions.
virtual ROL::Ptr< Vector > clone() const =0
Clone to make a new (uninitialized) vector.
virtual Real value(const Vector< Real > &x, Real &tol)=0
Compute value.
void initialize(Vector< Real > &x, const Vector< Real > &g, Objective< Real > &sobj, Objective< Real > &nobj, Vector< Real > &px, Vector< Real > &dg, std::ostream &outStream=std::cout)
virtual void prox(Vector< Real > &Pv, const Vector< Real > &v, Real t, Real &tol)
Defines the linear algebra or vector space interface.
virtual void update(const Vector< Real > &x, UpdateType type, int iter=-1)
Update objective function.
Objective_SerialSimOpt(const Ptr< Obj > &obj, const V &ui) z0_ zero()
void writeName(std::ostream &os) const override
Print step name.
virtual void gradient(Vector< Real > &g, const Vector< Real > &x, Real &tol)
Compute gradient.
void run(Vector< Real > &x, const Vector< Real > &g, Objective< Real > &sobj, Objective< Real > &nobj, std::ostream &outStream=std::cout) override
Run algorithm on unconstrained problems (Type-U). This general interface supports the use of dual opt...
Provides an interface to check status of optimization algorithms.
void writeOutput(std::ostream &os, bool write_header=false) const override
Print iterate status.
SpectralGradientAlgorithm(ParameterList &list)
virtual void set(const Vector &x)
Set where .
void writeHeader(std::ostream &os) const override
Print iterate header.
virtual void writeExitStatus(std::ostream &os) const
void initialize(const Vector< Real > &x, const Vector< Real > &g)