/usr/include/trilinos/ROL_Objective.hpp is in libtrilinos-rol-dev 12.10.1-3.
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// ************************************************************************
//
// Rapid Optimization Library (ROL) Package
// Copyright (2014) Sandia Corporation
//
// Under terms of Contract DE-AC04-94AL85000, there is a non-exclusive
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//
// 3. Neither the name of the Corporation nor the names of the
// contributors may be used to endorse or promote products derived from
// this software without specific prior written permission.
//
// THIS SOFTWARE IS PROVIDED BY SANDIA CORPORATION "AS IS" AND ANY
// EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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// @HEADER
#ifndef ROL_OBJECTIVE_H
#define ROL_OBJECTIVE_H
#include "ROL_Vector.hpp"
#include "ROL_Types.hpp"
#include <iostream>
/** @ingroup func_group
\class ROL::Objective
\brief Provides the interface to evaluate objective functions.
ROL's objective function interface is designed for Fr$eacute;chet differentiable
functionals \f$f:\mathcal{X}\to\mathbb{R}\f$, where \f$\mathcal{X}\f$ is a Banach
space. The basic operator interace, to be implemented by the user, requires:
\li #value -- objective function evaluation.
It is strongly recommended that the user additionally overload:
\li #gradient -- the objective function gradient -- the default is a finite-difference approximation;
\li #hessVec -- the action of the Hessian -- the default is a finite-difference approximation.
The user may also overload:
\li #update -- update the objective function at each new iteration;
\li #dirDeriv -- compute the directional derivative -- the default is a finite-difference approximation;
\li #invHessVec -- the action of the inverse Hessian;
\li #precond -- the action of a preconditioner for the Hessian.
---
*/
namespace ROL {
template <class Real>
class Objective {
public:
virtual ~Objective() {}
/** \brief Update objective function.
This function updates the objective function at new iterations.
@param[in] x is the new iterate.
@param[in] flag is true if the iterate has changed.
@param[in] iter is the outer algorithm iterations count.
*/
virtual void update( const Vector<Real> &x, bool flag = true, int iter = -1 ) {}
/** \brief Compute value.
This function returns the objective function value.
@param[in] x is the current iterate.
@param[in] tol is a tolerance for inexact objective function computation.
*/
virtual Real value( const Vector<Real> &x, Real &tol ) = 0;
/** \brief Compute gradient.
This function returns the objective function gradient.
@param[out] g is the gradient.
@param[in] x is the current iterate.
@param[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 \f$\{\phi_i\}\f$ for the optimization vectors x and
the definition of a basis \f$\{\psi_j\}\f$ for the dual optimization vectors (gradient vectors g).
The bases must be related through the Riesz map, i.e., \f$ R \{\phi_i\} = \{\psi_j\}\f$,
and this must be reflected in the implementation of the ROL::Vector::dual() method.
*/
virtual void gradient( Vector<Real> &g, const Vector<Real> &x, Real &tol ) ;
/** \brief Compute directional derivative.
This function returns the directional derivative of the objective function in the \f$d\f$ direction.
@param[in] x is the current iterate.
@param[in] d is the direction.
@param[in] tol is a tolerance for inexact objective function computation.
*/
virtual Real dirDeriv( const Vector<Real> &x, const Vector<Real> &d, Real &tol ) ;
/** \brief Apply Hessian approximation to vector.
This function applies the Hessian of the objective function to the vector \f$v\f$.
@param[out] hv is the the action of the Hessian on \f$v\f$.
@param[in] v is the direction vector.
@param[in] x is the current iterate.
@param[in] tol is a tolerance for inexact objective function computation.
*/
virtual void hessVec( Vector<Real> &hv, const Vector<Real> &v, const Vector<Real> &x, Real &tol );
/** \brief Apply inverse Hessian approximation to vector.
This function applies the inverse Hessian of the objective function to the vector \f$v\f$.
@param[out] hv is the action of the inverse Hessian on \f$v\f$.
@param[in] v is the direction vector.
@param[in] x is the current iterate.
@param[in] tol is a tolerance for inexact objective function computation.
*/
virtual void invHessVec( Vector<Real> &hv, const Vector<Real> &v, const Vector<Real> &x, Real &tol ) {
TEUCHOS_TEST_FOR_EXCEPTION(true, std::invalid_argument,
">>> ERROR (ROL::Objective): invHessVec not implemented!");
//hv.set(v.dual());
}
/** \brief Apply preconditioner to vector.
This function applies a preconditioner for the Hessian of the objective function to the vector \f$v\f$.
@param[out] Pv is the action of the Hessian preconditioner on \f$v\f$.
@param[in] v is the direction vector.
@param[in] x is the current iterate.
@param[in] tol is a tolerance for inexact objective function computation.
*/
virtual void precond( Vector<Real> &Pv, const Vector<Real> &v, const Vector<Real> &x, Real &tol ) {
Pv.set(v.dual());
}
/** \brief Finite-difference gradient check.
This function computes a sequence of one-sided finite-difference checks for the gradient.
At each step of the sequence, the finite difference step size is decreased. The output
compares the error
\f[
\left| \frac{f(x+td) - f(x)}{t} - \langle \nabla f(x),d\rangle_{\mathcal{X}^*,\mathcal{X}}\right|.
\f]
if the approximation is first order. More generally, difference approximation is
\f[
\frac{1}{t} \sum\limits_{i=1}^m w_i f(x+t c_i d)
\f]
where m = order+1, \f$w_i\f$ are the difference weights and \f$c_i\f$ are the difference steps
@param[in] x is an optimization variable.
@param[in] d is a direction vector.
@param[in] printToStream is a flag that turns on/off output.
@param[out] outStream is the output stream.
@param[in] numSteps is a parameter which dictates the number of finite difference steps.
@param[in] order is the order of the finite difference approximation (1,2,3,4)
*/
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 ) {
return checkGradient(x, x.dual(), d, printToStream, outStream, numSteps, order);
}
/** \brief Finite-difference gradient check.
This function computes a sequence of one-sided finite-difference checks for the gradient.
At each step of the sequence, the finite difference step size is decreased. The output
compares the error
\f[
\left| \frac{f(x+td) - f(x)}{t} - \langle \nabla f(x),d\rangle_{\mathcal{X}^*,\mathcal{X}}\right|.
\f]
if the approximation is first order. More generally, difference approximation is
\f[
\frac{1}{t} \sum\limits_{i=1}^m w_i f(x+t c_i d)
\f]
where m = order+1, \f$w_i\f$ are the difference weights and \f$c_i\f$ are the difference steps
@param[in] x is an optimization variable.
@param[in] g is used to create a temporary gradient vector.
@param[in] d is a direction vector.
@param[in] printToStream is a flag that turns on/off output.
@param[out] outStream is the output stream.
@param[in] numSteps is a parameter which dictates the number of finite difference steps.
@param[in] order is the order of the finite difference approximation (1,2,3,4)
*/
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 );
/** \brief Finite-difference gradient check with specified step sizes.
This function computes a sequence of one-sided finite-difference checks for the gradient.
At each step of the sequence, the finite difference step size is decreased. The output
compares the error
\f[
\left| \frac{f(x+td) - f(x)}{t} - \langle \nabla f(x),d\rangle_{\mathcal{X}^*,\mathcal{X}}\right|.
\f]
if the approximation is first order. More generally, difference approximation is
\f[
\frac{1}{t} \sum\limits_{i=1}^m w_i f(x+t c_i d)
\f]
where m = order+1, \f$w_i\f$ are the difference weights and \f$c_i\f$ are the difference steps
@param[in] x is an optimization variable.
@param[in] d is a direction vector.
@param[in] steps is vector of steps of user-specified size.
@param[in] printToStream is a flag that turns on/off output.
@param[out] outStream is the output stream.
@param[in] order is the order of the finite difference approximation (1,2,3,4)
*/
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 ) {
return checkGradient(x, x.dual(), d, steps, printToStream, outStream, order);
}
/** \brief Finite-difference gradient check with specified step sizes.
This function computes a sequence of one-sided finite-difference checks for the gradient.
At each step of the sequence, the finite difference step size is decreased. The output
compares the error
\f[
\left| \frac{f(x+td) - f(x)}{t} - \langle \nabla f(x),d\rangle_{\mathcal{X}^*,\mathcal{X}}\right|.
\f]
if the approximation is first order. More generally, difference approximation is
\f[
\frac{1}{t} \sum\limits_{i=1}^m w_i f(x+t c_i d)
\f]
where m = order+1, \f$w_i\f$ are the difference weights and \f$c_i\f$ are the difference steps
@param[in] x is an optimization variable.
@param[in] g is used to create a temporary gradient vector.
@param[in] d is a direction vector.
@param[in] steps is vector of steps of user-specified size.
@param[in] printToStream is a flag that turns on/off output.
@param[out] outStream is the output stream.
@param[in] order is the order of the finite difference approximation (1,2,3,4)
*/
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 );
/** \brief Finite-difference Hessian-applied-to-vector check.
This function computes a sequence of one-sided finite-difference checks for the Hessian.
At each step of the sequence, the finite difference step size is decreased. The output
compares the error
\f[
\left\| \frac{\nabla f(x+td) - \nabla f(x)}{t} - \nabla^2 f(x)d\right\|_{\mathcal{X}^*}.
\f]
if the approximation is first order. More generally, difference approximation is
\f[
\frac{1}{t} \sum\limits_{i=1}^m w_i \nabla f(x+t c_i d)
\f]
where m = order+1, \f$w_i\f$ are the difference weights and \f$c_i\f$ are the difference steps
@param[in] x is an optimization variable.
@param[in] d is a direction vector.
@param[in] printToStream is a flag that turns on/off output.
@param[out] outStream is the output stream.
@param[in] numSteps is a parameter which dictates the number of finite difference steps.
@param[in] order is the order of the finite difference approximation (1,2,3,4)
*/
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 ) {
return checkHessVec(x, x.dual(), v, printToStream, outStream, numSteps, order);
}
/** \brief Finite-difference Hessian-applied-to-vector check.
This function computes a sequence of one-sided finite-difference checks for the Hessian.
At each step of the sequence, the finite difference step size is decreased. The output
compares the error
\f[
\left\| \frac{\nabla f(x+td) - \nabla f(x)}{t} - \nabla^2 f(x)d\right\|_{\mathcal{X}^*}.
\f]
if the approximation is first order. More generally, difference approximation is
\f[
\frac{1}{t} \sum\limits_{i=1}^m w_i \nabla f(x+t c_i d)
\f]
where m = order+1, \f$w_i\f$ are the difference weights and \f$c_i\f$ are the difference steps
@param[in] x is an optimization variable.
@param[in] hv is used to create temporary gradient and Hessian-times-vector vectors.
@param[in] d is a direction vector.
@param[in] printToStream is a flag that turns on/off output.
@param[out] outStream is the output stream.
@param[in] numSteps is a parameter which dictates the number of finite difference steps.
@param[in] order is the order of the finite difference approximation (1,2,3,4)
*/
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) ;
/** \brief Finite-difference Hessian-applied-to-vector check with specified step sizes.
This function computes a sequence of one-sided finite-difference checks for the Hessian.
At each step of the sequence, the finite difference step size is decreased. The output
compares the error
\f[
\left\| \frac{\nabla f(x+td) - \nabla f(x)}{t} - \nabla^2 f(x)d\right\|_{\mathcal{X}^*}.
\f]
if the approximation is first order. More generally, difference approximation is
\f[
\frac{1}{t} \sum\limits_{i=1}^m w_i \nabla f(x+t c_i d)
\f]
where m = order+1, \f$w_i\f$ are the difference weights and \f$c_i\f$ are the difference steps
@param[in] x is an optimization variable.
@param[in] d is a direction vector.
@param[in] steps is vector of steps of user-specified size.
@param[in] printToStream is a flag that turns on/off output.
@param[out] outStream is the output stream.
@param[in] order is the order of the finite difference approximation (1,2,3,4)
*/
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 ) {
return checkHessVec(x, x, v, steps, printToStream, outStream, order);
}
/** \brief Finite-difference Hessian-applied-to-vector check with specified step sizes.
This function computes a sequence of one-sided finite-difference checks for the Hessian.
At each step of the sequence, the finite difference step size is decreased. The output
compares the error
\f[
\left\| \frac{\nabla f(x+td) - \nabla f(x)}{t} - \nabla^2 f(x)d\right\|_{\mathcal{X}^*}.
\f]
if the approximation is first order. More generally, difference approximation is
\f[
\frac{1}{t} \sum\limits_{i=1}^m w_i \nabla f(x+t c_i d)
\f]
where m = order+1, \f$w_i\f$ are the difference weights and \f$c_i\f$ are the difference steps
@param[in] x is an optimization variable.
@param[in] hv is used to create temporary gradient and Hessian-times-vector vectors.
@param[in] d is a direction vector.
@param[in] steps is vector of steps of user-specified size.
@param[in] printToStream is a flag that turns on/off output.
@param[out] outStream is the output stream.
@param[in] order is the order of the finite difference approximation (1,2,3,4)
*/
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) ;
/** \brief Hessian symmetry check.
This function checks the symmetry of the Hessian by comparing
\f[
\langle \nabla^2f(x)v,w\rangle_{\mathcal{X}^*,\mathcal{X}}
\quad\text{and}\quad
\langle \nabla^2f(x)w,v\rangle_{\mathcal{X}^*,\mathcal{X}}.
\f]
@param[in] x is an optimization variable.
@param[in] v is a direction vector.
@param[in] w is a direction vector.
@param[in] printToStream is a flag that turns on/off output.
@param[out] outStream is the output stream.
*/
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 ) {
return checkHessSym(x, x, v, w, printToStream, outStream);
}
/** \brief Hessian symmetry check.
This function checks the symmetry of the Hessian by comparing
\f[
\langle \nabla^2f(x)v,w\rangle_{\mathcal{X}^*,\mathcal{X}}
\quad\text{and}\quad
\langle \nabla^2f(x)w,v\rangle_{\mathcal{X}^*,\mathcal{X}}.
\f]
@param[in] x is an optimization variable.
@param[in] hv is used to create temporary Hessian-times-vector vectors.
@param[in] v is a direction vector.
@param[in] w is a direction vector.
@param[in] printToStream is a flag that turns on/off output.
@param[out] outStream is the output stream.
*/
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 );
// Definitions for parametrized (stochastic) objective functions
private:
std::vector<Real> param_;
protected:
const std::vector<Real> getParameter(void) const {
return param_;
}
public:
virtual void setParameter(const std::vector<Real> ¶m) {
param_.assign(param.begin(),param.end());
}
}; // class Objective
} // namespace ROL
// include templated definitions
#include <ROL_ObjectiveDef.hpp>
#endif
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