/usr/include/trilinos/ROL_TrustRegionStep.hpp is in libtrilinos-rol-dev 12.10.1-3.
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// ************************************************************************
//
// Rapid Optimization Library (ROL) Package
// Copyright (2014) Sandia Corporation
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#ifndef ROL_TRUSTREGIONSTEP_H
#define ROL_TRUSTREGIONSTEP_H
#include "ROL_Step.hpp"
#include "ROL_Types.hpp"
#include "ROL_Secant.hpp"
#include "ROL_TrustRegion.hpp"
#include <sstream>
#include <iomanip>
/** @ingroup step_group
\class ROL::TrustRegionStep
\brief Provides the interface to compute optimization steps
with trust regions.
Suppose \f$\mathcal{X}\f$ is a Hilbert space of
functions mapping \f$\Xi\f$ to \f$\mathbb{R}\f$. For example,
\f$\Xi\subset\mathbb{R}^n\f$ and \f$\mathcal{X}=L^2(\Xi)\f$ or
\f$\Xi = \{1,\ldots,n\}\f$ and \f$\mathcal{X}=\mathbb{R}^n\f$. We
assume \f$f:\mathcal{X}\to\mathbb{R}\f$ is twice-continuously Fréchet
differentiable and \f$a,\,b\in\mathcal{X}\f$ with \f$a\le b\f$ almost
everywhere in \f$\Xi\f$. Note that these trust-region algorithms will also work
with secant approximations of the Hessian.
This step applies to unconstrained and bound constrained optimization problems,
\f[
\min_x\quad f(x) \qquad\text{and}\qquad \min_x\quad f(x)\quad\text{s.t.}\quad a\le x\le b,
\f]
respectively.
For unconstrained problems, given the \f$k\f$-th iterate \f$x_k\f$ the trial step
\f$s_k\f$ is computed by approximately solving the trust-region subproblem
\f[
\min_{s} \frac{1}{2}\langle B_k s, s\rangle_{\mathcal{X}} + \langle g_k,s\rangle_{\mathcal{X}}
\quad\text{s.t.}\quad \|s\|_{\mathcal{X}} \le \Delta_k
\f]
where \f$B_k\in L(\mathcal{X},\mathcal{X})\f$, \f$g_k\approx\nabla f(x_k)\f$, and \f$\Delta_k > 0\f$.
The approximate minimizer \f$s_k\f$ must satisfy the fraction of Cauchy decrease condition
\f[
-\frac{1}{2}\langle B_k s, s\rangle_{\mathcal{X}} - \langle g_k,s\rangle_{\mathcal{X}}
\ge \kappa_0 \|g_k\|_{\mathcal{X}}
\min\left\{\,\Delta_k,\,
\frac{\|g_k\|_{\mathcal{X}}}{1+\|B_k\|_{L(\mathcal{X},\mathcal{X}})}\,\right\}
\f]
for some \f$\kappa_0>0\f$ independent of \f$k\f$.
ROL's trust-region algorithm allows for both inexact objective function and gradient evaluation.
The user must ensure that the inexact objective function, \f$f_k\f$ satisfies
\f[
|(f(x_k+s_k)-f_k(x_k+s_k)) - (f(x_k)-f_k(x_k))| \le
\eta_1 \min\{\,-\frac{1}{2}\langle B_k s, s\rangle_{\mathcal{X}} - \langle g_k,s\rangle_{\mathcal{X}},
\,r_k\,\}
\f]
where \f$\eta_1\f$ is the step acceptance threshold and \f$r_k\f$ is a user-defined forcing sequence of
positive numbers converging to zero. The inexact gradient, \f$g_k\f$, must satisfy
\f[
\|g_k-\nabla J(x_k)\|_{\mathcal{X}} \le \kappa_1\min\{\,\|g_k\|_{\mathcal{X}},\,\Delta_k\,\}
\f]
where \f$\kappa_1 > 0\f$ is independent of \f$k\f$.
For bound constrained problems, ROL employs projected Newton-type methods.
For these methods, ROL requires the notion of an active set of an iterate \f$x_k\f$,
\f[
\mathcal{A}_k = \{\, \xi\in\Xi\,:\,x_k(\xi) = a(\xi)\,\}\cap
\{\, \xi\in\Xi\,:\,x_k(\xi) = b(\xi)\,\}.
\f]
Given \f$\mathcal{A}_k\f$ and a gradient approximation \f$g_k\f$, we define the binding set as
\f[
\mathcal{B}_k = \{\, \xi\in\Xi\,:\,x_k(\xi) = a(\xi) \;\text{and}\; -g_k(\xi) < 0 \,\}\cap
\{\, \xi\in\Xi\,:\,x_k(\xi) = b(\xi) \;\text{and}\; -g_k(\xi) > 0 \,\}.
\f]
The binding set contains the values of \f$\xi\in\Xi\f$ such that if \f$x_k(\xi)\f$ is on a
bound, then \f$(x_k+s_k)(\xi)\f$ will violate bound. Using these definitions, ROL
prunes the variables in the binding set and runs a standard trust-region subproblem solver on the
free variables. ROL then must perform a projected search to ensure the fraction of Cauchy decrease
condition is satisfied.
TrustRegionStep implements a number of algorithms for both bound constrained and unconstrained
optimization. These algorithms are: Cauchy Point, Dogleg, Double Dogleg, and Truncated CG.
Each of these methods can be run using a secant approximation of the Hessian.
These methods are chosen through the ETrustRegion enum.
*/
namespace ROL {
template <class Real>
class TrustRegionStep : public Step<Real> {
private:
// ADDITIONAL VECTOR STORAGE
Teuchos::RCP<Vector<Real> > xnew_; ///< Container for updated iteration vector.
Teuchos::RCP<Vector<Real> > xold_; ///< Container for previous iteration vector.
Teuchos::RCP<Vector<Real> > gp_; ///< Container for previous gradient vector.
// TRUST REGION INFORMATION
Teuchos::RCP<TrustRegion<Real> > trustRegion_; ///< Container for trust-region solver object.
Teuchos::RCP<TrustRegionModel<Real> > model_; ///< Container for trust-region model.
ETrustRegion etr_; ///< Trust-region subproblem solver type.
ETrustRegionModel TRmodel_; ///< Trust-region subproblem model type.
Real delMax_; ///< Maximum trust-region radius.
ETrustRegionFlag TRflag_; ///< Trust-region exit flag.
int SPflag_; ///< Subproblem solver termination flag.
int SPiter_; ///< Subproblem solver iteration count.
bool bndActive_; ///< Flag whether bound is activated.
// SECANT INFORMATION
Teuchos::RCP<Secant<Real> > secant_; ///< Container for secant approximation.
ESecant esec_; ///< Secant type.
bool useSecantHessVec_; ///< Flag whether to use a secant Hessian.
bool useSecantPrecond_; ///< Flag whether to use a secant preconditioner.
// BOUND CONSTRAINED PARAMETERS
Real scaleEps_; ///< Scaling for epsilon-active sets.
bool useProjectedGrad_; ///< Flag whether to use the projected gradient criticality measure.
// POST SMOOTHING PARAMETERS
Real alpha_init_; ///< Initial line-search parameter for projected methods.
int max_fval_; ///< Maximum function evaluations in line-search for projected methods.
Real mu_; ///< Post-Smoothing tolerance for projected methods.
Real beta_; ///< Post-Smoothing rate for projected methods.
// COLEMAN-LI PARAMETERS
Real stepBackMax_;
Real stepBackScale_;
bool singleReflect_;
// INEXACT COMPUTATION PARAMETERS
std::vector<bool> useInexact_; ///< Flags for inexact (0) objective function, (1) gradient, (2) Hessian.
Real scale0_; ///< Scale for inexact gradient computation.
Real scale1_; ///< Scale for inexact gradient computation.
// VERBOSITY SETTING
int verbosity_; ///< Print additional information to screen if > 0.
/** \brief Parse input ParameterList.
This function sets trust region specific parameters specified in the user
supplied ParameterList.
@param[in] parlist is the user-supplied ParameterList.
*/
void parseParameterList(Teuchos::ParameterList &parlist) {
Teuchos::RCP<StepState<Real> > step_state = Step<Real>::getState();
// Trust-Region Parameters
Teuchos::ParameterList &slist = parlist.sublist("Step");
Teuchos::ParameterList &list = slist.sublist("Trust Region");
step_state->searchSize = list.get("Initial Radius", static_cast<Real>(-1));
delMax_ = list.get("Maximum Radius", static_cast<Real>(1.e8));
// Inexactness Information
Teuchos::ParameterList &glist = parlist.sublist("General");
useInexact_.clear();
useInexact_.push_back(glist.get("Inexact Objective Function", false));
useInexact_.push_back(glist.get("Inexact Gradient", false));
useInexact_.push_back(glist.get("Inexact Hessian-Times-A-Vector", false));
// Trust-Region Inexactness Parameters
Teuchos::ParameterList &ilist = list.sublist("Inexact").sublist("Gradient");
scale0_ = ilist.get("Tolerance Scaling", static_cast<Real>(0.1));
scale1_ = ilist.get("Relative Tolerance", static_cast<Real>(2));
// Initialize Trust Region Subproblem Solver Object
etr_ = StringToETrustRegion(list.get("Subproblem Solver", "Dogleg"));
TRmodel_ = StringToETrustRegionModel(list.get("Subproblem Model", "Kelley-Sachs"));
useProjectedGrad_ = glist.get("Projected Gradient Criticality Measure", false);
trustRegion_ = TrustRegionFactory<Real>(parlist);
// Scale for epsilon active sets
scaleEps_ = glist.get("Scale for Epsilon Active Sets", static_cast<Real>(1));
verbosity_ = glist.get("Print Verbosity", 0);
// Post-smoothing parameters
max_fval_ = list.sublist("Post-Smoothing").get("Function Evaluation Limit", 20);
alpha_init_ = list.sublist("Post-Smoothing").get("Initial Step Size", static_cast<Real>(1));
mu_ = list.sublist("Post-Smoothing").get("Tolerance", static_cast<Real>(0.9999));
beta_ = list.sublist("Post-Smoothing").get("Rate", static_cast<Real>(0.01));
// Coleman-Li parameters
stepBackMax_ = list.sublist("Coleman-Li").get("Maximum Step Back", static_cast<Real>(0.9999));
stepBackScale_ = list.sublist("Coleman-Li").get("Maximum Step Scale", static_cast<Real>(1));
singleReflect_ = list.sublist("Coleman-Li").get("Single Reflection", true);
}
/** \brief Update gradient to iteratively satisfy inexactness condition.
This function attempts to ensure that the inexact gradient condition,
\f[
\|g_k-\nabla J(x_k)\|_{\mathcal{X}} \le \kappa_1\min\{\,\|g_k\|_{\mathcal{X}},\,\Delta_k\,\},
\f]
is satisfied. This function works under the assumption that the gradient function returns
a gradient approximation which satisfies the error tolerance prescribed by the tol input
parameter.
@param[in] x is the current optimization variable.
@param[in] obj is the objective function.
@param[in] bnd is the bound constraint.
@param[in,out] algo_state is the algorithm state.
*/
void updateGradient( Vector<Real> &x, Objective<Real> &obj, BoundConstraint<Real> &bnd,
AlgorithmState<Real> &algo_state ) {
Real oem2(1.e-2), one(1), oe4(1.e4);
Teuchos::RCP<StepState<Real> > state = Step<Real>::getState();
if ( useInexact_[1] ) {
Real c = scale0_*std::max(oem2,std::min(one,oe4*algo_state.gnorm));
Real gtol1 = c*(state->searchSize);
Real gtol0 = scale1_*gtol1 + one;
while ( gtol0 > gtol1*scale1_ ) {
obj.gradient(*(state->gradientVec),x,gtol1);
algo_state.gnorm = computeCriticalityMeasure(*(state->gradientVec),x,bnd);
gtol0 = gtol1;
c = scale0_*std::max(oem2,std::min(one,oe4*algo_state.gnorm));
gtol1 = c*std::min(algo_state.gnorm,state->searchSize);
}
algo_state.ngrad++;
}
else {
Real gtol = std::sqrt(ROL_EPSILON<Real>());
obj.gradient(*(state->gradientVec),x,gtol);
algo_state.ngrad++;
algo_state.gnorm = computeCriticalityMeasure(*(state->gradientVec),x,bnd);
}
}
/** \brief Compute the criticality measure.
This function computes either the norm of the gradient projected onto the tangent cone or
the norm of \f$x_k - P_{[a,b]}(x_k-g_k)\f$.
@param[in] g is the current gradient.
@param[in] x is the current iterate.
@param[in] bnd is the bound constraint.
*/
Real computeCriticalityMeasure( const Vector<Real> &g, const Vector<Real> &x, BoundConstraint<Real> &bnd ) {
if ( bnd.isActivated() ) {
if ( useProjectedGrad_ ) {
gp_->set(g);
bnd.computeProjectedGradient( *gp_, x );
return gp_->norm();
}
else {
Real one(1);
xnew_->set(x);
xnew_->axpy(-one,g.dual());
bnd.project(*xnew_);
xnew_->axpy(-one,x);
return xnew_->norm();
}
}
else {
return g.norm();
}
}
public:
using Step<Real>::initialize;
using Step<Real>::compute;
using Step<Real>::update;
virtual ~TrustRegionStep() {}
/** \brief Constructor.
Standard constructor to build a TrustRegionStep object. Algorithmic
specifications are passed in through a Teuchos::ParameterList.
@param[in] parlist is a parameter list containing algorithmic specifications
*/
TrustRegionStep( Teuchos::ParameterList & parlist )
: Step<Real>(),
xnew_(Teuchos::null), xold_(Teuchos::null), gp_(Teuchos::null),
trustRegion_(Teuchos::null), model_(Teuchos::null),
etr_(TRUSTREGION_DOGLEG), TRmodel_(TRUSTREGION_MODEL_KELLEYSACHS),
delMax_(1e8), TRflag_(TRUSTREGION_FLAG_SUCCESS),
SPflag_(0), SPiter_(0), bndActive_(false),
secant_(Teuchos::null), esec_(SECANT_LBFGS),
useSecantHessVec_(false), useSecantPrecond_(false),
scaleEps_(1), useProjectedGrad_(false),
alpha_init_(1), max_fval_(20), mu_(0.9999), beta_(0.01),
stepBackMax_(0.9999), stepBackScale_(1), singleReflect_(true),
scale0_(1), scale1_(1),
verbosity_(0) {
// Parse input parameterlist
parseParameterList(parlist);
// Create secant object
Teuchos::ParameterList &glist = parlist.sublist("General");
esec_ = StringToESecant(glist.sublist("Secant").get("Type","Limited-Memory BFGS"));
useSecantPrecond_ = glist.sublist("Secant").get("Use as Preconditioner", false);
useSecantHessVec_ = glist.sublist("Secant").get("Use as Hessian", false);
secant_ = SecantFactory<Real>(parlist);
}
/** \brief Constructor.
Constructor to build a TrustRegionStep object with a user-defined
secant object. Algorithmic specifications are passed in through
a Teuchos::ParameterList.
@param[in] secant is a user-defined secant object
@param[in] parlist is a parameter list containing algorithmic specifications
*/
TrustRegionStep( Teuchos::RCP<Secant<Real> > &secant, Teuchos::ParameterList &parlist )
: Step<Real>(),
xnew_(Teuchos::null), xold_(Teuchos::null), gp_(Teuchos::null),
trustRegion_(Teuchos::null), model_(Teuchos::null),
etr_(TRUSTREGION_DOGLEG), TRmodel_(TRUSTREGION_MODEL_KELLEYSACHS),
delMax_(1e8), TRflag_(TRUSTREGION_FLAG_SUCCESS),
SPflag_(0), SPiter_(0), bndActive_(false),
secant_(Teuchos::null), esec_(SECANT_LBFGS),
useSecantHessVec_(false), useSecantPrecond_(false),
scaleEps_(1), useProjectedGrad_(false),
alpha_init_(1), max_fval_(20), mu_(0.9999), beta_(0.01),
stepBackMax_(0.9999), stepBackScale_(1), singleReflect_(true),
scale0_(1), scale1_(1),
verbosity_(0) {
// Parse input parameterlist
parseParameterList(parlist);
// Create secant object
Teuchos::ParameterList &glist = parlist.sublist("General");
useSecantPrecond_ = glist.sublist("Secant").get("Use as Preconditioner", false);
useSecantHessVec_ = glist.sublist("Secant").get("Use as Hessian", false);
if ( secant_ == Teuchos::null ) {
Teuchos::ParameterList Slist;
Slist.sublist("General").sublist("Secant").set("Type","Limited-Memory BFGS");
Slist.sublist("General").sublist("Secant").set("Maximum Storage",10);
secant_ = SecantFactory<Real>(Slist);
}
}
/** \brief Initialize step.
This function initializes the information necessary to run the trust-region algorithm.
@param[in] x is the initial guess for the optimization vector.
@param[in] obj is the objective function.
@param[in] bnd is the bound constraint.
@param[in] algo_state is the algorithm state.
*/
void initialize( Vector<Real> &x, const Vector<Real> &s, const Vector<Real> &g,
Objective<Real> &obj, BoundConstraint<Real> &bnd,
AlgorithmState<Real> &algo_state ) {
Real p1(0.1), oe10(1.e10), zero(0), one(1), half(0.5), three(3), two(2), six(6);
Teuchos::RCP<StepState<Real> > step_state = Step<Real>::getState();
bndActive_ = bnd.isActivated();
trustRegion_->initialize(x,s,g);
Real htol = std::sqrt(ROL_EPSILON<Real>());
Real ftol = p1*ROL_OVERFLOW<Real>();
step_state->descentVec = s.clone();
step_state->gradientVec = g.clone();
if ( bnd.isActivated() ) {
// Make initial guess feasible
bnd.project(x);
xnew_ = x.clone();
xold_ = x.clone();
// Make initial guess strictly feasible
if ( TRmodel_ == TRUSTREGION_MODEL_COLEMANLI ) {
xold_->set(*bnd.getUpperVectorRCP()); // u
xold_->axpy(-one,*bnd.getLowerVectorRCP()); // u - l
Real minDiff = static_cast<Real>(1e-1)
* std::min(one, half * xold_->reduce(Elementwise::ReductionMin<Real>()));
class LowerFeasible : public Elementwise::BinaryFunction<Real> {
private:
const Real eps_;
public:
LowerFeasible(const Real eps) : eps_(eps) {}
Real apply( const Real &x, const Real &y ) const {
const Real tol = static_cast<Real>(100)*ROL_EPSILON<Real>();
return (x < y+tol) ? y+eps_ : x;
}
};
x.applyBinary(LowerFeasible(minDiff), *bnd.getLowerVectorRCP());
class UpperFeasible : public Elementwise::BinaryFunction<Real> {
private:
const Real eps_;
public:
UpperFeasible(const Real eps) : eps_(eps) {}
Real apply( const Real &x, const Real &y ) const {
const Real tol = static_cast<Real>(100)*ROL_EPSILON<Real>();
return (x > y-tol) ? y-eps_ : x;
}
};
x.applyBinary(UpperFeasible(minDiff), *bnd.getUpperVectorRCP());
}
}
gp_ = g.clone();
// Update approximate gradient and approximate objective function.
obj.update(x,true,algo_state.iter);
updateGradient(x,obj,bnd,algo_state);
algo_state.snorm = oe10;
algo_state.value = obj.value(x,ftol);
algo_state.nfval++;
// Try to apply inverse Hessian
if ( !useSecantHessVec_ &&
(etr_ == TRUSTREGION_DOGLEG || etr_ == TRUSTREGION_DOUBLEDOGLEG) ) {
try {
Teuchos::RCP<Vector<Real> > v = g.clone();
Teuchos::RCP<Vector<Real> > hv = x.clone();
obj.invHessVec(*hv,*v,x,htol);
}
catch (std::exception &e) {
useSecantHessVec_ = true;
}
}
// Evaluate Objective Function at Cauchy Point
if ( step_state->searchSize <= zero ) {
Teuchos::RCP<Vector<Real> > Bg = g.clone();
if ( useSecantHessVec_ ) {
secant_->applyB(*Bg,(step_state->gradientVec)->dual());
}
else {
obj.hessVec(*Bg,(step_state->gradientVec)->dual(),x,htol);
}
Real gBg = Bg->dot(*(step_state->gradientVec));
Real alpha = one;
if ( gBg > ROL_EPSILON<Real>() ) {
alpha = algo_state.gnorm*algo_state.gnorm/gBg;
}
// Evaluate the objective function at the Cauchy point
Teuchos::RCP<Vector<Real> > cp = s.clone();
cp->set((step_state->gradientVec)->dual());
cp->scale(-alpha);
Teuchos::RCP<Vector<Real> > xcp = x.clone();
xcp->set(x);
xcp->plus(*cp);
if ( bnd.isActivated() ) {
bnd.project(*xcp);
}
obj.update(*xcp);
Real fnew = obj.value(*xcp,ftol); // MUST DO SOMETHING HERE WITH FTOL
algo_state.nfval++;
// Perform cubic interpolation to determine initial trust region radius
Real gs = cp->dot((step_state->gradientVec)->dual());
Real a = fnew - algo_state.value - gs - half*alpha*alpha*gBg;
if ( std::abs(a) < ROL_EPSILON<Real>() ) {
// a = 0 implies the objective is quadratic in the negative gradient direction
step_state->searchSize = std::min(alpha*algo_state.gnorm,delMax_);
}
else {
Real b = half*alpha*alpha*gBg;
Real c = gs;
if ( b*b-three*a*c > ROL_EPSILON<Real>() ) {
// There is at least one critical point
Real t1 = (-b-std::sqrt(b*b-three*a*c))/(three*a);
Real t2 = (-b+std::sqrt(b*b-three*a*c))/(three*a);
if ( six*a*t1 + two*b > zero ) {
// t1 is the minimizer
step_state->searchSize = std::min(t1*alpha*algo_state.gnorm,delMax_);
}
else {
// t2 is the minimizer
step_state->searchSize = std::min(t2*alpha*algo_state.gnorm,delMax_);
}
}
else {
step_state->searchSize = std::min(alpha*algo_state.gnorm,delMax_);
}
}
}
}
/** \brief Compute step.
Computes a trial step, \f$s_k\f$ by solving the trust-region subproblem.
The trust-region subproblem solver is defined by the enum ETrustRegion.
@param[out] s is the computed trial step
@param[in] x is the current iterate
@param[in] obj is the objective function
@param[in] bnd are the bound constraints
@param[in] algo_state contains the current state of the algorithm
*/
void compute( Vector<Real> &s, const Vector<Real> &x, Objective<Real> &obj, BoundConstraint<Real> &bnd,
AlgorithmState<Real> &algo_state ) {
// Get step state
Teuchos::RCP<StepState<Real> > step_state = Step<Real>::getState();
// Build trust-region model
if (bnd.isActivated()) {
if ( TRmodel_ == TRUSTREGION_MODEL_KELLEYSACHS ) {
// Real eps = scaleEps_*algo_state.gnorm;
Real eps = scaleEps_ * std::min(std::pow(algo_state.gnorm,static_cast<Real>(0.75)),
static_cast<Real>(0.01));
model_ = Teuchos::rcp(new ROL::KelleySachsModel<Real>(obj,
bnd,
x,
*(step_state->gradientVec),
eps,
secant_,
useSecantPrecond_,
useSecantHessVec_));
}
else if ( TRmodel_ == TRUSTREGION_MODEL_COLEMANLI ) {
model_ = Teuchos::rcp(new ROL::ColemanLiModel<Real>(obj,
bnd,
x,
*(step_state->gradientVec),
secant_,
useSecantPrecond_,
useSecantHessVec_,
step_state->searchSize,
stepBackMax_,
stepBackScale_,
singleReflect_));
}
else {
TEUCHOS_TEST_FOR_EXCEPTION( true, std::invalid_argument,
">>> ERROR (ROL::TrustRegionStep): Invalid trust-region model!");
}
}
else {
model_ = Teuchos::rcp(new ROL::TrustRegionModel<Real>(obj,
x,
*(step_state->gradientVec),
secant_,
useSecantPrecond_,
useSecantHessVec_));
}
// Minimize trust-region model over trust-region constraint
SPflag_ = 0; SPiter_ = 0;
trustRegion_->run(s,algo_state.snorm,SPflag_,SPiter_,step_state->searchSize,*model_);
}
/** \brief Update step, if successful.
Given a trial step, \f$s_k\f$, this function updates \f$x_{k+1}=x_k+s_k\f$.
This function also updates the secant approximation.
@param[in,out] x is the updated iterate
@param[in] s is the computed trial step
@param[in] obj is the objective function
@param[in] bnd are the bound constraints
@param[in] algo_state contains the current state of the algorithm
*/
void update( Vector<Real> &x,
const Vector<Real> &s,
Objective<Real> &obj,
BoundConstraint<Real> &bnd,
AlgorithmState<Real> &algo_state ) {
// Get step state
Teuchos::RCP<StepState<Real> > state = Step<Real>::getState();
// Store previous step for constraint computations
if ( bnd.isActivated() ) {
xold_->set(x);
}
// Update trust-region information;
// Performs a hard update on the objective function
TRflag_ = TRUSTREGION_FLAG_SUCCESS;
state->nfval = 0;
state->ngrad = 0;
Real fold = algo_state.value;
Real fnew(0);
algo_state.iter++;
trustRegion_->update(x,fnew,state->searchSize,state->nfval,state->ngrad,TRflag_,
s,algo_state.snorm,fold,*(state->gradientVec),algo_state.iter,
obj,bnd,*model_);
algo_state.nfval += state->nfval;
algo_state.ngrad += state->ngrad;
// If step is accepted ...
// Compute new gradient and update secant storage
if ( TRflag_ == TRUSTREGION_FLAG_SUCCESS ||
TRflag_ == TRUSTREGION_FLAG_POSPREDNEG ) {
// Perform line search (smoothing) to ensure decrease
if ( bnd.isActivated() && TRmodel_ == TRUSTREGION_MODEL_KELLEYSACHS ) {
Real tol = std::sqrt(ROL_EPSILON<Real>());
// Compute new gradient
obj.gradient(*gp_,x,tol); // MUST DO SOMETHING HERE WITH TOL
algo_state.ngrad++;
// Compute smoothed step
Real alpha(1);
xnew_->set(x);
xnew_->axpy(-alpha*alpha_init_,gp_->dual());
bnd.project(*xnew_);
// Compute new objective value
obj.update(*xnew_,true,algo_state.iter);
Real ftmp = obj.value(*xnew_,tol); // MUST DO SOMETHING HERE WITH TOL
algo_state.nfval++;
// Perform smoothing
int cnt = 0;
alpha = static_cast<Real>(1)/alpha_init_;
while ( (fnew-ftmp) <= mu_*(fnew-fold) ) {
xnew_->set(x);
xnew_->axpy(-alpha*alpha_init_,gp_->dual());
bnd.project(*xnew_);
obj.update(*xnew_,true,algo_state.iter);
ftmp = obj.value(*xnew_,tol); // MUST DO SOMETHING HERE WITH TOL
algo_state.nfval++;
if ( cnt >= max_fval_ ) {
break;
}
alpha *= beta_;
cnt++;
}
// Store objective function and iteration information
fnew = ftmp;
x.set(*xnew_);
}
// Store previous gradient for secant update
if ( useSecantHessVec_ || useSecantPrecond_ ) {
gp_->set(*(state->gradientVec));
}
// Update objective function and approximate model
updateGradient(x,obj,bnd,algo_state);
// Update secant information
if ( useSecantHessVec_ || useSecantPrecond_ ) {
if ( bnd.isActivated() ) { // Compute new constrained step
xnew_->set(x);
xnew_->axpy(-static_cast<Real>(1),*xold_);
secant_->updateStorage(x,*(state->gradientVec),*gp_,*xnew_,algo_state.snorm,algo_state.iter+1);
}
else {
secant_->updateStorage(x,*(state->gradientVec),*gp_,s,algo_state.snorm,algo_state.iter+1);
}
}
// Update algorithm state
(algo_state.iterateVec)->set(x);
}
// Update algorithm state
algo_state.value = fnew;
}
/** \brief Print iterate header.
This function produces a string containing header information.
*/
std::string printHeader( void ) const {
std::stringstream hist;
if(verbosity_>0) {
hist << std::string(114,'-') << "\n";
hist << "Trust-Region status output definitions\n\n";
hist << " iter - Number of iterates (steps taken) \n";
hist << " value - Objective function value \n";
hist << " gnorm - Norm of the gradient\n";
hist << " snorm - Norm of the step (update to optimization vector)\n";
hist << " delta - Trust-Region radius\n";
hist << " #fval - Number of times the objective function was evaluated\n";
hist << " #grad - Number of times the gradient was computed\n";
hist << "\n";
hist << " tr_flag - Trust-Region flag" << "\n";
for( int flag = TRUSTREGION_FLAG_SUCCESS; flag != TRUSTREGION_FLAG_UNDEFINED; ++flag ) {
hist << " " << NumberToString(flag) << " - "
<< ETrustRegionFlagToString(static_cast<ETrustRegionFlag>(flag)) << "\n";
}
if( etr_ == TRUSTREGION_TRUNCATEDCG ) {
hist << "\n";
hist << " iterCG - Number of Truncated CG iterations\n\n";
hist << " flagGC - Trust-Region Truncated CG flag" << "\n";
for( int flag = CG_FLAG_SUCCESS; flag != CG_FLAG_UNDEFINED; ++flag ) {
hist << " " << NumberToString(flag) << " - "
<< ECGFlagToString(static_cast<ECGFlag>(flag)) << "\n";
}
}
hist << std::string(114,'-') << "\n";
}
hist << " ";
hist << std::setw(6) << std::left << "iter";
hist << std::setw(15) << std::left << "value";
hist << std::setw(15) << std::left << "gnorm";
hist << std::setw(15) << std::left << "snorm";
hist << std::setw(15) << std::left << "delta";
hist << std::setw(10) << std::left << "#fval";
hist << std::setw(10) << std::left << "#grad";
hist << std::setw(10) << std::left << "tr_flag";
if ( etr_ == TRUSTREGION_TRUNCATEDCG ) {
hist << std::setw(10) << std::left << "iterCG";
hist << std::setw(10) << std::left << "flagCG";
}
hist << "\n";
return hist.str();
}
/** \brief Print step name.
This function produces a string containing the algorithmic step information.
*/
std::string printName( void ) const {
std::stringstream hist;
hist << "\n" << ETrustRegionToString(etr_) << " Trust-Region Solver";
if ( useSecantPrecond_ || useSecantHessVec_ ) {
if ( useSecantPrecond_ && !useSecantHessVec_ ) {
hist << " with " << ESecantToString(esec_) << " Preconditioning\n";
}
else if ( !useSecantPrecond_ && useSecantHessVec_ ) {
hist << " with " << ESecantToString(esec_) << " Hessian Approximation\n";
}
else {
hist << " with " << ESecantToString(esec_) << " Preconditioning and Hessian Approximation\n";
}
}
else {
hist << "\n";
}
if ( bndActive_ ) {
hist << "Trust-Region Model: " << ETrustRegionModelToString(TRmodel_) << "\n";
}
return hist.str();
}
/** \brief Print iterate status.
This function prints the iteration status.
@param[in] algo_state is the current state of the algorithm
@param[in] printHeader if ste to true will print the header at each iteration
*/
std::string print( AlgorithmState<Real> & algo_state, bool print_header = false ) const {
const Teuchos::RCP<const StepState<Real> >& step_state = Step<Real>::getStepState();
std::stringstream hist;
hist << std::scientific << std::setprecision(6);
if ( algo_state.iter == 0 ) {
hist << printName();
}
if ( print_header ) {
hist << printHeader();
}
if ( algo_state.iter == 0 ) {
hist << " ";
hist << std::setw(6) << std::left << algo_state.iter;
hist << std::setw(15) << std::left << algo_state.value;
hist << std::setw(15) << std::left << algo_state.gnorm;
hist << std::setw(15) << std::left << " ";
hist << std::setw(15) << std::left << step_state->searchSize;
hist << "\n";
}
else {
hist << " ";
hist << std::setw(6) << std::left << algo_state.iter;
hist << std::setw(15) << std::left << algo_state.value;
hist << std::setw(15) << std::left << algo_state.gnorm;
hist << std::setw(15) << std::left << algo_state.snorm;
hist << std::setw(15) << std::left << step_state->searchSize;
hist << std::setw(10) << std::left << algo_state.nfval;
hist << std::setw(10) << std::left << algo_state.ngrad;
hist << std::setw(10) << std::left << TRflag_;
if ( etr_ == TRUSTREGION_TRUNCATEDCG ) {
hist << std::setw(10) << std::left << SPiter_;
hist << std::setw(10) << std::left << SPflag_;
}
hist << "\n";
}
return hist.str();
}
}; // class Step
} // namespace ROL
#endif
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