simplex_internal.hpp File Reference

#include <Eigen/Dense>
#include <string>
#include <vector>
#include "simplex_internal.hxx"

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Classes
struct	EigenOpt::simplex::internal::VariableDomain
	Auxiliay structure to store the domain of a variable. More...

Namespaces
namespace	EigenOpt
	Main namespace of this project, containing all utilities.
namespace	EigenOpt::simplex
	Contains functions to solve linear programming problems with the Simplex method.
namespace	EigenOpt::simplex::internal
	Utility functions used by the Simplex algorithm.

Functions
template<class Scalar >
bool	EigenOpt::simplex::internal::deduce_variables_domains (const Eigen::Matrix< Scalar, Eigen::Dynamic, Eigen::Dynamic > &C, const Eigen::Matrix< Scalar, Eigen::Dynamic, 1 > &d, const Scalar &small_number, std::vector< VariableDomain > &domains, std::string &halt_reason)
	Given a set of inequality constraints, deduce the domain of the decision variables.
template<class Scalar >
Eigen::Matrix< Scalar, Eigen::Dynamic, Eigen::Dynamic >	EigenOpt::simplex::internal::transformation_matrix_from_domains (const std::vector< VariableDomain > &domains)
	Calculate a transformation matrix so that \(\bm{x}=\bm{T}\bm{w}\), \(w \geq 0\).
template<class Scalar >
bool	EigenOpt::simplex::internal::transformation_matrix (const Eigen::Matrix< Scalar, Eigen::Dynamic, Eigen::Dynamic > &C, const Eigen::Matrix< Scalar, Eigen::Dynamic, 1 > &d, const Scalar &small_number, Eigen::Matrix< Scalar, Eigen::Dynamic, Eigen::Dynamic > &T, std::string &halt_reason)
	Calculate a transformation matrix so that \(\bm{x}=\bm{T}\bm{w}\), \(w \geq 0\).
template<class Scalar >
void	EigenOpt::simplex::internal::create_tableau (const Eigen::Matrix< Scalar, Eigen::Dynamic, Eigen::Dynamic > &C, const Eigen::Matrix< Scalar, Eigen::Dynamic, 1 > &d, Eigen::Matrix< Scalar, Eigen::Dynamic, Eigen::Dynamic > &tableau, std::vector< int > &basic_variables)
	Create a Simplex Tableau given a set of inequality constraints.
template<class Scalar >
void	EigenOpt::simplex::internal::eliminate_objective (Eigen::Matrix< Scalar, Eigen::Dynamic, Eigen::Dynamic > &tableau, const std::vector< int > &basic_variables)
	Use Gaussian elimination on the last row of the tableau.
template<class Scalar >
void	EigenOpt::simplex::internal::pivot (Eigen::Matrix< Scalar, Eigen::Dynamic, Eigen::Dynamic > &tableau, int entering_variable, int leaving_variable)
	Perform a pivot operation between a basic and a non-basic variable.
template<class Scalar >
bool	EigenOpt::simplex::internal::simplex (Eigen::Matrix< Scalar, Eigen::Dynamic, Eigen::Dynamic > &tableau, std::vector< int > &basic_variables, const Scalar &small_number, std::string &halt_reason)
	Perform successive pivot operations until a termination condition is met.
template<class Scalar >
bool	EigenOpt::simplex::internal::two_steps_method (const Eigen::Matrix< Scalar, Eigen::Dynamic, 1 > &objective, Eigen::Matrix< Scalar, Eigen::Dynamic, Eigen::Dynamic > &tableau, std::vector< int > &basic_variables, unsigned int na, const Scalar &small_number, std::string &halt_reason)
	Solve a minimization problem using the two-steps Simplex method.
template<class Scalar >
bool	EigenOpt::simplex::internal::penalty_method (const Eigen::Matrix< Scalar, Eigen::Dynamic, 1 > &objective, Eigen::Matrix< Scalar, Eigen::Dynamic, Eigen::Dynamic > &tableau, std::vector< int > &basic_variables, unsigned int na, const Scalar &small_number, const Scalar &large_number, std::string &halt_reason)
	Solve a minimization problem using the penalty Simplex method.