libtrilinos-rol-dev 12.12.1-5 / usr / include / trilinos / ROL_AugmentedLagrangianStep.hpp

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#ifndef ROL_AUGMENTEDLAGRANGIANSTEP_H
#define ROL_AUGMENTEDLAGRANGIANSTEP_H

#include "ROL_AugmentedLagrangian.hpp"
#include "ROL_Vector.hpp"
#include "ROL_Objective.hpp"
#include "ROL_BoundConstraint.hpp"
#include "ROL_EqualityConstraint.hpp"
#include "ROL_Types.hpp"
#include "ROL_Algorithm.hpp"
#include "ROL_StatusTest.hpp"
#include "ROL_Step.hpp"
#include "ROL_LineSearchStep.hpp"
#include "ROL_TrustRegionStep.hpp"
#include "Teuchos_ParameterList.hpp"

/** @ingroup step_group
    \class ROL::AugmentedLagrangianStep
    \brief Provides the interface to compute augmented Lagrangian steps.
*/


namespace ROL {

template <class Real>
class AugmentedLagrangianStep : public Step<Real> {
private:
  Teuchos::RCP<Algorithm<Real> > algo_;
  Teuchos::RCP<Vector<Real> > x_; 

  Teuchos::ParameterList parlist_;
  // Lagrange multiplier update
  bool scaleLagrangian_;
  Real minPenaltyReciprocal_;
  Real minPenaltyLowerBound_;
  Real penaltyUpdate_;
  Real maxPenaltyParam_;
  // Optimality tolerance update
  Real optIncreaseExponent_;
  Real optDecreaseExponent_;
  Real optToleranceInitial_;
  Real optTolerance_;
  // Feasibility tolerance update
  Real feasIncreaseExponent_;
  Real feasDecreaseExponent_;
  Real feasToleranceInitial_;
  Real feasTolerance_;
  // Subproblem information
  bool print_;
  int maxit_;
  int subproblemIter_;
  std::string subStep_;
  Real outerOptTolerance_;
  Real outerFeasTolerance_;
  Real outerStepTolerance_;

  Real computeGradient(Vector<Real> &g, const Vector<Real> &x,
                       const Real mu, Objective<Real> &obj,
                       BoundConstraint<Real> &bnd) {
    AugmentedLagrangian<Real> &augLag
      = Teuchos::dyn_cast<AugmentedLagrangian<Real> >(obj);
    Real gnorm = 0., tol = std::sqrt(ROL_EPSILON<Real>());
    augLag.gradient(g,x,tol);
    if ( scaleLagrangian_ ) {
      g.scale(mu);
    }
    // Compute norm of projected gradient
    if (bnd.isActivated()) {
      x_->set(x);
      x_->axpy(-1.,g.dual());
      bnd.project(*x_);
      x_->axpy(-1.,x);
      gnorm = x_->norm();
    }
    else {
      gnorm = g.norm();
    }
    return gnorm;
  }

public:

  using Step<Real>::initialize;
  using Step<Real>::compute;
  using Step<Real>::update;

  ~AugmentedLagrangianStep() {}

  AugmentedLagrangianStep(Teuchos::ParameterList &parlist)
    : Step<Real>(), algo_(Teuchos::null),
      x_(Teuchos::null), parlist_(parlist), subproblemIter_(0) {
    Real one(1), p1(0.1), p9(0.9), ten(1.e1), oe8(1.e8), oem8(1.e-8);
    Teuchos::ParameterList& sublist = parlist.sublist("Step").sublist("Augmented Lagrangian");
    Step<Real>::getState()->searchSize = sublist.get("Initial Penalty Parameter",ten);
    // Multiplier update parameters
    scaleLagrangian_      = sublist.get("Use Scaled Augmented Lagrangian",          false);
    minPenaltyLowerBound_ = sublist.get("Penalty Parameter Reciprocal Lower Bound", p1);
    minPenaltyReciprocal_ = p1;
    penaltyUpdate_        = sublist.get("Penalty Parameter Growth Factor",          ten);
    maxPenaltyParam_      = sublist.get("Maximum Penalty Parameter",                oe8);
    // Optimality tolerance update
    optIncreaseExponent_ = sublist.get("Optimality Tolerance Update Exponent",    one);
    optDecreaseExponent_ = sublist.get("Optimality Tolerance Decrease Exponent",  one);
    optToleranceInitial_ = sublist.get("Initial Optimality Tolerance",            one);
    // Feasibility tolerance update    
    feasIncreaseExponent_ = sublist.get("Feasibility Tolerance Update Exponent",   p1);
    feasDecreaseExponent_ = sublist.get("Feasibility Tolerance Decrease Exponent", p9);
    feasToleranceInitial_ = sublist.get("Initial Feasibility Tolerance",           one);
    // Subproblem information
    print_   = sublist.get("Print Intermediate Optimization History", false);
    maxit_   = sublist.get("Subproblem Iteration Limit",              1000);
    subStep_ = sublist.get("Subproblem Step Type",                    "Trust Region");
    parlist_.sublist("Status Test").set("Iteration Limit",maxit_);
    // Outer iteration tolerances
    outerFeasTolerance_ = parlist.sublist("Status Test").get("Constraint Tolerance", oem8);
    outerOptTolerance_  = parlist.sublist("Status Test").get("Gradient Tolerance",   oem8);
    outerStepTolerance_ = parlist.sublist("Status Test").get("Step Tolerance",       oem8);
  }

  /** \brief Initialize step with equality constraint.
  */
  void initialize( Vector<Real> &x, const Vector<Real> &g, Vector<Real> &l, const Vector<Real> &c,
                   Objective<Real> &obj, EqualityConstraint<Real> &con, BoundConstraint<Real> &bnd,
                   AlgorithmState<Real> &algo_state ) {
    AugmentedLagrangian<Real> &augLag
      = Teuchos::dyn_cast<AugmentedLagrangian<Real> >(obj);
    // Initialize step state
    Teuchos::RCP<StepState<Real> > state = Step<Real>::getState();
    state->descentVec    = x.clone();
    state->gradientVec   = g.clone();
    state->constraintVec = c.clone();
    // Initialize additional storage
    x_ = x.clone();
    // Initialize the algorithm state
    algo_state.nfval = 0;
    algo_state.ncval = 0;
    algo_state.ngrad = 0;
    // Project x onto the feasible set
    if ( bnd.isActivated() ) {
      bnd.project(x);
    }
    bnd.update(x,true,algo_state.iter);
    // Update objective and constraint.
    augLag.update(x,true,algo_state.iter);
    algo_state.value = augLag.getObjectiveValue(x);
    algo_state.gnorm = computeGradient(*(state->gradientVec),x,state->searchSize,obj,bnd);
    augLag.getConstraintVec(*(state->constraintVec),x);
    algo_state.cnorm = (state->constraintVec)->norm();
    // Update evaluation counters
    algo_state.ncval += augLag.getNumberConstraintEvaluations();
    algo_state.nfval += augLag.getNumberFunctionEvaluations();
    algo_state.ngrad += augLag.getNumberGradientEvaluations();
    // Initialize intermediate stopping tolerances
    Real one(1), TOL(1.e-2);
    minPenaltyReciprocal_ = std::min(one/state->searchSize,minPenaltyLowerBound_);
    optTolerance_  = std::max(TOL*outerOptTolerance_,
                              optToleranceInitial_*std::pow(minPenaltyReciprocal_,optDecreaseExponent_));
    optTolerance_  = std::min(optTolerance_,TOL*algo_state.gnorm);
    feasTolerance_ = std::max(TOL*outerFeasTolerance_,
                              feasToleranceInitial_*std::pow(minPenaltyReciprocal_,feasDecreaseExponent_));
  }

  /** \brief Compute step (equality and bound constraints).
  */
  void compute( Vector<Real> &s, const Vector<Real> &x, const Vector<Real> &l,
                Objective<Real> &obj, EqualityConstraint<Real> &con, 
                BoundConstraint<Real> &bnd, AlgorithmState<Real> &algo_state ) {
    Real one(1);
    AugmentedLagrangian<Real> &augLag
      = Teuchos::dyn_cast<AugmentedLagrangian<Real> >(obj);
    parlist_.sublist("Status Test").set("Gradient Tolerance",optTolerance_);
    parlist_.sublist("Status Test").set("Step Tolerance",1.e-6*optTolerance_);
    algo_ = Teuchos::rcp(new Algorithm<Real>(subStep_,parlist_,false));
    x_->set(x);
    if ( bnd.isActivated() ) {
      algo_->run(*x_,augLag,bnd,print_);
    }
    else {
      algo_->run(*x_,augLag,print_);
    }
    s.set(*x_); s.axpy(-one,x);
    subproblemIter_ = (algo_->getState())->iter;
  }

  /** \brief Update step, if successful (equality and bound constraints).
  */
  void update( Vector<Real> &x, Vector<Real> &l, const Vector<Real> &s,
               Objective<Real> &obj, EqualityConstraint<Real> &con,
               BoundConstraint<Real> &bnd,
               AlgorithmState<Real> &algo_state ) {
    Real one(1), oem2(1.e-2);
    AugmentedLagrangian<Real> &augLag
      = Teuchos::dyn_cast<AugmentedLagrangian<Real> >(obj);
    Teuchos::RCP<StepState<Real> > state = Step<Real>::getState();
    // Update the step and store in state
    x.plus(s);
    algo_state.iterateVec->set(x);
    state->descentVec->set(s);
    algo_state.snorm = s.norm();
    algo_state.iter++;
    // Update objective function value
    algo_state.value = augLag.getObjectiveValue(x);
    // Update constraint value
    augLag.getConstraintVec(*(state->constraintVec),x);
    algo_state.cnorm = (state->constraintVec)->norm();
    // Compute gradient of the augmented Lagrangian
    algo_state.gnorm = computeGradient(*(state->gradientVec),x,state->searchSize,obj,bnd);
    // Update evaluation counters
    algo_state.nfval += augLag.getNumberFunctionEvaluations();
    algo_state.ngrad += augLag.getNumberGradientEvaluations();
    algo_state.ncval += augLag.getNumberConstraintEvaluations();
    // Update objective function and constraints
    augLag.update(x,true,algo_state.iter);
    bnd.update(x,true,algo_state.iter);
    // Update multipliers
    minPenaltyReciprocal_ = std::min(one/state->searchSize,minPenaltyLowerBound_);
    if ( algo_state.cnorm < feasTolerance_ ) {
      l.axpy(state->searchSize,(state->constraintVec)->dual());
      optTolerance_  = std::max(oem2*outerOptTolerance_,
                       optTolerance_*std::pow(minPenaltyReciprocal_,optIncreaseExponent_));
      feasTolerance_ = std::max(oem2*outerFeasTolerance_,
                       feasTolerance_*std::pow(minPenaltyReciprocal_,feasIncreaseExponent_));
      // Update Algorithm State
      algo_state.snorm += state->searchSize*algo_state.cnorm;
      algo_state.lagmultVec->set(l);
    }
    else {
      state->searchSize = std::min(penaltyUpdate_*state->searchSize,maxPenaltyParam_);
      optTolerance_     = std::max(oem2*outerOptTolerance_,
                          optToleranceInitial_*std::pow(minPenaltyReciprocal_,optDecreaseExponent_));
      feasTolerance_    = std::max(oem2*outerFeasTolerance_,
                          feasToleranceInitial_*std::pow(minPenaltyReciprocal_,feasDecreaseExponent_));
    }
    augLag.reset(l,state->searchSize);
  }

  /** \brief Print iterate header.
  */
  std::string printHeader( void ) const {
    std::stringstream hist;
    hist << "  ";
    hist << std::setw(6)  << std::left << "iter";
    hist << std::setw(15) << std::left << "fval";
    hist << std::setw(15) << std::left << "cnorm";
    hist << std::setw(15) << std::left << "gLnorm";
    hist << std::setw(15) << std::left << "snorm";
    hist << std::setw(10) << std::left << "penalty";
    hist << std::setw(10) << std::left << "feasTol";
    hist << std::setw(10) << std::left << "optTol";
    hist << std::setw(8) << std::left << "#fval";
    hist << std::setw(8) << std::left << "#grad";
    hist << std::setw(8) << std::left << "#cval";
    hist << std::setw(8) << std::left << "subIter";
    hist << "\n";
    return hist.str();
  }

  /** \brief Print step name.
  */
  std::string printName( void ) const {
    std::stringstream hist;
    hist << "\n" << " Augmented Lagrangian solver";
    hist << "\n";
    return hist.str();
  }

  /** \brief Print iterate status.
  */
  std::string print( AlgorithmState<Real> &algo_state, bool pHeader = false ) const {
    std::stringstream hist;
    hist << std::scientific << std::setprecision(6);
    if ( algo_state.iter == 0 ) {
      hist << printName();
    }
    if ( pHeader ) {
      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.cnorm;
      hist << std::setw(15) << std::left << algo_state.gnorm;
      hist << std::setw(15) << std::left << " ";
      hist << std::scientific << std::setprecision(2);
      hist << std::setw(10) << std::left << Step<Real>::getStepState()->searchSize;
      hist << std::setw(10) << std::left << std::max(feasTolerance_,outerFeasTolerance_);
      hist << std::setw(10) << std::left << std::max(optTolerance_,outerOptTolerance_);
      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.cnorm;
      hist << std::setw(15) << std::left << algo_state.gnorm;
      hist << std::setw(15) << std::left << algo_state.snorm;
      hist << std::scientific << std::setprecision(2);
      hist << std::setw(10) << std::left << Step<Real>::getStepState()->searchSize;
      hist << std::setw(10) << std::left << feasTolerance_;
      hist << std::setw(10) << std::left << optTolerance_;
      hist << std::scientific << std::setprecision(6);
      hist << std::setw(8) << std::left << algo_state.nfval;
      hist << std::setw(8) << std::left << algo_state.ngrad;
      hist << std::setw(8) << std::left << algo_state.ncval;
      hist << std::setw(8) << std::left << subproblemIter_;
      hist << "\n";
    }
    return hist.str();
  }

  /** \brief Compute step for bound constraints; here only to satisfy the
             interface requirements, does nothing, needs refactoring.
  */
  void compute( Vector<Real> &s, const Vector<Real> &x, Objective<Real> &obj,
                        BoundConstraint<Real> &con,
                        AlgorithmState<Real> &algo_state ) {}

  /** \brief Update step, for bound constraints; here only to satisfy the
             interface requirements, does nothing, needs refactoring.
  */
  void update( Vector<Real> &x, const Vector<Real> &s, Objective<Real> &obj,
                       BoundConstraint<Real> &con,
                       AlgorithmState<Real> &algo_state ) {}

}; // class AugmentedLagrangianStep

} // namespace ROL

#endif