// Copyright (C) 2008 Davis E. King (davis@dlib.net)
// License: Boost Software License See LICENSE.txt for the full license.
#undef DLIB_OPTIMIZATIOn_SEARCH_STRATEGIES_ABSTRACT_
#ifdef DLIB_OPTIMIZATIOn_SEARCH_STRATEGIES_ABSTRACT_
#include <cmath>
#include <limits>
#include "../matrix/matrix_abstract.h"
#include "../algs.h"
namespace dlib
{
/*
A good discussion of the search strategies in this file can be found in the
following book: Numerical Optimization by Nocedal and Wright.
*/
// ----------------------------------------------------------------------------------------
class cg_search_strategy
{
/*!
WHAT THIS OBJECT REPRESENTS
This object represents a strategy for determining which direction
a line search should be carried out along. This particular object
is an implementation of the Polak-Ribiere conjugate gradient method
for determining this direction.
This method uses an amount of memory that is linear in the number
of variables to be optimized. So it is capable of handling problems
with a very large number of variables. However, it is generally
not as good as the L-BFGS algorithm (which is defined below in
the lbfgs_search_strategy class).
!*/
public:
cg_search_strategy(
);
/*!
ensures
- This object is properly initialized and ready to generate
search directions.
!*/
double get_wolfe_rho (
) const;
/*!
ensures
- returns the value of the Wolfe rho parameter that should be used when
this search strategy is used with the line_search() function.
!*/
double get_wolfe_sigma (
) const;
/*!
ensures
- returns the value of the Wolfe sigma parameter that should be used when
this search strategy is used with the line_search() function.
!*/
unsigned long get_max_line_search_iterations (
) const;
/*!
ensures
- returns the value of the max iterations parameter that should be used when
this search strategy is used with the line_search() function.
!*/
template <typename T>
const matrix<double,0,1>& get_next_direction (
const T& x,
const double funct_value,
const T& funct_derivative
);
/*!
requires
- this function is only called once per search iteration
- for some objective function f():
- x == the search point for the current iteration
- funct_value == f(x)
- funct_derivative == derivative(f)(x)
ensures
- Assuming that a line search is going to be conducted starting from the point x,
this function returns the direction in which the search should proceed.
!*/
};
// ----------------------------------------------------------------------------------------
class bfgs_search_strategy
{
/*!
WHAT THIS OBJECT REPRESENTS
This object represents a strategy for determining which direction
a line search should be carried out along. This particular object
is an implementation of the BFGS quasi-newton method for determining
this direction.
This method uses an amount of memory that is quadratic in the number
of variables to be optimized. It is generally very effective but
if your problem has a very large number of variables then it isn't
appropriate. Instead You should try the lbfgs_search_strategy.
!*/
public:
bfgs_search_strategy(
);
/*!
ensures
- This object is properly initialized and ready to generate
search directions.
!*/
double get_wolfe_rho (
) const;
/*!
ensures
- returns the value of the Wolfe rho parameter that should be used when
this search strategy is used with the line_search() function.
!*/
double get_wolfe_sigma (
) const;
/*!
ensures
- returns the value of the Wolfe sigma parameter that should be used when
this search strategy is used with the line_search() function.
!*/
unsigned long get_max_line_search_iterations (
) const;
/*!
ensures
- returns the value of the max iterations parameter that should be used when
this search strategy is used with the line_search() function.
!*/
template <typename T>
const matrix<double,0,1>& get_next_direction (
const T& x,
const double funct_value,
const T& funct_derivative
);
/*!
requires
- this function is only called once per search iteration
- for some objective function f():
- x == the search point for the current iteration
- funct_value == f(x)
- funct_derivative == derivative(f)(x)
ensures
- Assuming that a line search is going to be conducted starting from the point x,
this function returns the direction in which the search should proceed.
!*/
};
// ----------------------------------------------------------------------------------------
class lbfgs_search_strategy
{
/*!
WHAT THIS OBJECT REPRESENTS
This object represents a strategy for determining which direction
a line search should be carried out along. This particular object
is an implementation of the L-BFGS quasi-newton method for determining
this direction.
This method uses an amount of memory that is linear in the number
of variables to be optimized. This makes it an excellent method
to use when an optimization problem has a large number of variables.
!*/
public:
explicit lbfgs_search_strategy(
unsigned long max_size
);
/*!
requires
- max_size > 0
ensures
- This object is properly initialized and ready to generate
search directions.
- L-BFGS works by remembering a certain number of position and gradient
pairs. It uses this remembered information to compute search directions.
The max_size argument determines how many of these pairs will be remembered.
Typically, using between 3 and 30 pairs performs well for many problems.
!*/
double get_wolfe_rho (
) const;
/*!
ensures
- returns the value of the Wolfe rho parameter that should be used when
this search strategy is used with the line_search() function.
!*/
double get_wolfe_sigma (
) const;
/*!
ensures
- returns the value of the Wolfe sigma parameter that should be used when
this search strategy is used with the line_search() function.
!*/
unsigned long get_max_line_search_iterations (
) const;
/*!
ensures
- returns the value of the max iterations parameter that should be used when
this search strategy is used with the line_search() function.
!*/
template <typename T>
const matrix<double,0,1>& get_next_direction (
const T& x,
const double funct_value,
const T& funct_derivative
);
/*!
requires
- this function is only called once per search iteration
- for some objective function f():
- x == the search point for the current iteration
- funct_value == f(x)
- funct_derivative == derivative(f)(x)
ensures
- Assuming that a line search is going to be conducted starting from the point x,
this function returns the direction in which the search should proceed.
!*/
};
// ----------------------------------------------------------------------------------------
template <
typename hessian_funct
>
class newton_search_strategy_obj
{
/*!
REQUIREMENTS ON hessian_funct
Objects of hessian_funct type must be function objects which
take a single argument and return a dlib::matrix of doubles. The
single argument must be a dlib::matrix capable of representing
column vectors of doubles. hessian_funct must also be copy
constructable.
WHAT THIS OBJECT REPRESENTS
This object represents a strategy for determining which direction
a line search should be carried out along. This particular object
is an implementation of the newton method for determining this
direction. That is, it uses the following formula to determine
the direction:
search_direction = -inv(hessian(x))*derivative
!*/
public:
explicit newton_search_strategy_obj(
const hessian_funct& hess
);
/*!
ensures
- This object is properly initialized and ready to generate
search directions.
- hess will be used by this object to generate the needed hessian
matrices every time get_next_direction() is called.
!*/
double get_wolfe_rho (
) const;
/*!
ensures
- returns the value of the Wolfe rho parameter that should be used when
this search strategy is used with the line_search() function.
!*/
double get_wolfe_sigma (
) const;
/*!
ensures
- returns the value of the Wolfe sigma parameter that should be used when
this search strategy is used with the line_search() function.
!*/
unsigned long get_max_line_search_iterations (
) const;
/*!
ensures
- returns the value of the max iterations parameter that should be used when
this search strategy is used with the line_search() function.
!*/
template <typename T>
const matrix<double,0,1> get_next_direction (
const T& x,
const double funct_value,
const T& funct_derivative
);
/*!
requires
- for some objective function f():
- x == the search point for the current iteration
- funct_value == f(x)
- funct_derivative == derivative(f)(x)
ensures
- Assuming that a line search is going to be conducted starting from the
point x, this function returns the direction in which the search should
proceed.
- In particular, the search direction will be given by:
- search_direction = -inv(hessian(x))*funct_derivative
!*/
};
template <typename hessian_funct>
newton_search_strategy_obj<hessian_funct> newton_search_strategy (
hessian_funct hessian
) { return newton_search_strategy_obj<hessian_funct>(hessian); }
/*!
ensures
- constructs and returns a newton_search_strategy_obj.
This function is just a helper to make the syntax for creating
these objects a little simpler.
!*/
// ----------------------------------------------------------------------------------------
}
#endif // DLIB_OPTIMIZATIOn_SEARCH_STRATEGIES_ABSTRACT_