/usr/include/trilinos/ROL_AugmentedLagrangian_SimOpt.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_AUGMENTEDLAGRANGIAN_SIMOPT_H
#define ROL_AUGMENTEDLAGRANGIAN_SIMOPT_H
#include "ROL_Objective_SimOpt.hpp"
#include "ROL_EqualityConstraint_SimOpt.hpp"
#include "ROL_QuadraticPenalty_SimOpt.hpp"
#include "ROL_Vector.hpp"
#include "ROL_Types.hpp"
#include "Teuchos_RCP.hpp"
#include <iostream>
/** @ingroup func_group
\class ROL::AugmentedLagrangian_SimOpt
\brief Provides the interface to evaluate the SimOpt augmented Lagrangian.
This class implements the SimOpt augmented Lagrangian functional for use with
ROL::Reduced_AugmentedLagrangian_SimOpt. Given a function
\f$f:\mathcal{U}\times\mathcal{Z}\to\mathbb{R}\f$ and an equality constraint
\f$c:\mathcal{U}\times\mathcal{Z}\to\mathcal{C}\f$, the augmented Lagrangian functional is
\f[
L_A(u,z,\lambda,\mu) = f(u,z) +
\langle \lambda, c(u,z)\rangle_{\mathcal{C}^*,\mathcal{C}} +
\frac{\mu}{2} \langle \mathfrak{R}c(u,z),c(u,z)\rangle_{\mathcal{C}^*,\mathcal{C}}
\f]
where \f$\lambda\in\mathcal{C}^*\f$ denotes the Lagrange multiplier estimate,
\f$\mu > 0\f$ is the penalty parameter and
\f$\mathfrak{R}\in\mathcal{L}(\mathcal{C},\mathcal{C}^*)\f$ is the Riesz operator
on the constraint space.
This implementation permits the scaling of \f$L_A\f$ by \f$\mu^{-1}\f$ and also
permits the Hessian approximation
\f[
\nabla^2_{uu} L_A(u,z,\lambda,\mu)v \approx \nabla^2_{uu} f(u,z) v
+ \mu c_u(u,z)^*\mathfrak{R} c_u(u,z)v,
\quad
\nabla^2_{uz} L_A(u,z,\lambda,\mu)v \approx \nabla^2_{uz} f(u,z) v
+ \mu c_u(u,z)^*\mathfrak{R} c_z(u,z)v,
\f]
\f[
\nabla^2_{zu} L_A(u,z,\lambda,\mu)v \approx \nabla^2_{zu} f(u,z) v
+ \mu c_z(u,z)^*\mathfrak{R} c_u(u,z)v,
\quad\text{and}\quad
\nabla^2_{zz} L_A(u,z,\lambda,\mu)v \approx \nabla^2_{zz} f(u,z) v
+ \mu c_z(u,z)^*\mathfrak{R} c_z(u,z)v,
\f]
---
*/
namespace ROL {
template <class Real>
class AugmentedLagrangian_SimOpt : public Objective_SimOpt<Real> {
private:
// Required for Augmented Lagrangian definition
const Teuchos::RCP<Objective_SimOpt<Real> > obj_;
Teuchos::RCP<QuadraticPenalty_SimOpt<Real> > pen_;
Real penaltyParameter_;
// Auxiliary storage
Teuchos::RCP<Vector<Real> > dualSimVector_;
Teuchos::RCP<Vector<Real> > dualOptVector_;
// Objective and constraint evaluations
Real fval_;
Teuchos::RCP<Vector<Real> > gradient1_;
Teuchos::RCP<Vector<Real> > gradient2_;
// Evaluation counters
int nfval_;
int ngval_;
// User defined options
bool scaleLagrangian_;
// Flags to recompute quantities
bool isValueComputed_;
bool isGradient1Computed_;
bool isGradient2Computed_;
public:
AugmentedLagrangian_SimOpt(const Teuchos::RCP<Objective_SimOpt<Real> > &obj,
const Teuchos::RCP<EqualityConstraint_SimOpt<Real> > &con,
const Vector<Real> &multiplier,
const Real penaltyParameter,
const Vector<Real> &simVec,
const Vector<Real> &optVec,
const Vector<Real> &conVec,
Teuchos::ParameterList &parlist)
: obj_(obj), penaltyParameter_(penaltyParameter),
fval_(0), nfval_(0), ngval_(0), isValueComputed_(false),
isGradient1Computed_(false), isGradient2Computed_(false) {
gradient1_ = simVec.dual().clone();
gradient2_ = optVec.dual().clone();
dualSimVector_ = simVec.dual().clone();
dualOptVector_ = optVec.dual().clone();
Teuchos::ParameterList& sublist = parlist.sublist("Step").sublist("Augmented Lagrangian");
scaleLagrangian_ = sublist.get("Use Scaled Augmented Lagrangian", false);
int HessianApprox = sublist.get("Level of Hessian Approximation", 0);
pen_ = Teuchos::rcp(new QuadraticPenalty_SimOpt<Real>(con,multiplier,penaltyParameter,simVec,optVec,conVec,scaleLagrangian_,HessianApprox));
}
virtual void update( const Vector<Real> &u, const Vector<Real> &z, bool flag = true, int iter = -1 ) {
obj_->update(u,z,flag,iter);
pen_->update(u,z,flag,iter);
isValueComputed_ = (flag ? false : isValueComputed_);
isGradient1Computed_ = (flag ? false : isGradient1Computed_);
isGradient2Computed_ = (flag ? false : isGradient2Computed_);
}
virtual Real value( const Vector<Real> &u, const Vector<Real> &z, Real &tol ) {
// Compute objective function value
if ( !isValueComputed_ ) {
fval_ = obj_->value(u,z,tol); nfval_++;
isValueComputed_ = true;
}
// Compute penalty term
Real pval = pen_->value(u,z,tol);
// Compute augmented Lagrangian
Real val = fval_;
if (scaleLagrangian_) {
val /= penaltyParameter_;
}
return val + pval;
}
virtual void gradient_1( Vector<Real> &g, const Vector<Real> &u, const Vector<Real> &z, Real &tol ) {
// Compute objective function gradient
if ( !isGradient1Computed_ ) {
obj_->gradient_1(*gradient1_,u,z,tol); ngval_++;
isGradient1Computed_ = true;
}
g.set(*gradient1_);
// Compute gradient of penalty
pen_->gradient_1(*dualSimVector_,u,z,tol);
// Compute gradient of Augmented Lagrangian
if ( scaleLagrangian_ ) {
g.scale(static_cast<Real>(1)/penaltyParameter_);
}
g.plus(*dualSimVector_);
}
virtual void gradient_2( Vector<Real> &g, const Vector<Real> &u, const Vector<Real> &z, Real &tol ) {
// Compute objective function gradient
if ( !isGradient2Computed_ ) {
obj_->gradient_2(*gradient2_,u,z,tol); ngval_++;
isGradient2Computed_ = true;
}
g.set(*gradient2_);
// Compute gradient of penalty
pen_->gradient_2(*dualOptVector_,u,z,tol);
// Compute gradient of Augmented Lagrangian
if ( scaleLagrangian_ ) {
g.scale(static_cast<Real>(1)/penaltyParameter_);
}
g.plus(*dualOptVector_);
}
virtual void hessVec_11( Vector<Real> &hv, const Vector<Real> &v,
const Vector<Real> &u, const Vector<Real> &z, Real &tol ) {
// Apply objective Hessian to a vector
obj_->hessVec_11(hv,v,u,z,tol);
// Apply penalty Hessian to a vector
pen_->hessVec_11(*dualSimVector_,v,u,z,tol);
// Build hessVec of Augmented Lagrangian
if ( scaleLagrangian_ ) {
hv.scale(static_cast<Real>(1)/penaltyParameter_);
}
hv.plus(*dualSimVector_);
}
virtual void hessVec_12( Vector<Real> &hv, const Vector<Real> &v,
const Vector<Real> &u, const Vector<Real> &z, Real &tol ) {
// Apply objective Hessian to a vector
obj_->hessVec_12(hv,v,u,z,tol);
// Apply penalty Hessian to a vector
pen_->hessVec_12(*dualSimVector_,v,u,z,tol);
// Build hessVec of Augmented Lagrangian
if ( scaleLagrangian_ ) {
hv.scale(static_cast<Real>(1)/penaltyParameter_);
}
hv.plus(*dualSimVector_);
}
virtual void hessVec_21( Vector<Real> &hv, const Vector<Real> &v,
const Vector<Real> &u, const Vector<Real> &z, Real &tol ) {
// Apply objective Hessian to a vector
obj_->hessVec_21(hv,v,u,z,tol);
// Apply penalty Hessian to a vector
pen_->hessVec_21(*dualOptVector_,v,u,z,tol);
// Build hessVec of Augmented Lagrangian
if ( scaleLagrangian_ ) {
hv.scale(static_cast<Real>(1)/penaltyParameter_);
}
hv.plus(*dualOptVector_);
}
virtual void hessVec_22( Vector<Real> &hv, const Vector<Real> &v,
const Vector<Real> &u, const Vector<Real> &z, Real &tol ) {
// Apply objective Hessian to a vector
obj_->hessVec_22(hv,v,u,z,tol);
// Apply penalty Hessian to a vector
pen_->hessVec_22(*dualOptVector_,v,u,z,tol);
// Build hessVec of Augmented Lagrangian
if ( scaleLagrangian_ ) {
hv.scale(static_cast<Real>(1)/penaltyParameter_);
}
hv.plus(*dualOptVector_);
}
// Return objective function value
virtual Real getObjectiveValue(const Vector<Real> &u, const Vector<Real> &z) {
Real tol = std::sqrt(ROL_EPSILON<Real>());
// Evaluate objective function value
if ( !isValueComputed_ ) {
fval_ = obj_->value(u,z,tol); nfval_++;
isValueComputed_ = true;
}
return fval_;
}
// Return constraint value
virtual void getConstraintVec(Vector<Real> &c, const Vector<Real> &u, const Vector<Real> &z) {
pen_->getConstraintVec(c,u,z);
}
// Return total number of constraint evaluations
virtual int getNumberConstraintEvaluations(void) const {
return pen_->getNumberConstraintEvaluations();
}
// Return total number of objective evaluations
virtual int getNumberFunctionEvaluations(void) const {
return nfval_;
}
// Return total number of gradient evaluations
virtual int getNumberGradientEvaluations(void) const {
return ngval_;
}
// Reset with upated penalty parameter
virtual void reset(const Vector<Real> &multiplier, const Real penaltyParameter) {
nfval_ = 0; ngval_ = 0;
pen_->reset(multiplier,penaltyParameter);
}
}; // class AugmentedLagrangian
} // namespace ROL
#endif
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