// 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. */ // ---------------------------------------------------------------------------------------- classcg_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. !*/doubleget_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. !*/doubleget_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. !*/unsignedlongget_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, constdoublefunct_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. !*/}; // ---------------------------------------------------------------------------------------- classbfgs_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. !*/doubleget_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. !*/doubleget_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. !*/unsignedlongget_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, constdoublefunct_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. !*/}; // ---------------------------------------------------------------------------------------- classlbfgs_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: explicitlbfgs_search_strategy(unsignedlongmax_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. !*/doubleget_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. !*/doubleget_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. !*/unsignedlongget_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, constdoublefunct_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 > classnewton_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: explicitnewton_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. !*/doubleget_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. !*/doubleget_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. !*/unsignedlongget_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, constdoublefunct_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_