Simplex.H File Reference

Simplex algorithm for linear programming. More...

#include <limits>
#include <fstream>
#include <vector>
#include <chrono>
#include <tpl_dynMat.H>
#include <tpl_dynDlist.H>
#include <ah-errors.H>

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Classes
struct	Aleph::SimplexStats
	Execution statistics for the Simplex algorithm. More...
struct	Aleph::SensitivityRange< T >
	Sensitivity analysis result for a coefficient. More...
class	Aleph::Simplex< T >
	Linear program solver using the Simplex method. More...
class	Aleph::RevisedSimplex< T >
	Revised Simplex algorithm for linear programming. More...
struct	Aleph::RevisedSimplex< T >::EtaMatrix

Namespaces
namespace	Aleph
	Main namespace for Aleph-w library functions.

Enumerations
enum class	Aleph::ConstraintType { Aleph::LE , Aleph::GE , Aleph::EQ }
	Constraint type for linear programming. More...
enum class	Aleph::OptimizationType { Aleph::Maximize , Aleph::Minimize }
	Optimization direction for linear programming. More...

Detailed Description

Simplex algorithm for linear programming.

Implements the Simplex method for solving linear programming problems: maximize/minimize c'x subject to Ax ≤ b, x ≥ 0.

Features

• Two-phase simplex method
• Handles unbounded and infeasible cases
• Big-M method for artificial variables
• Dual Simplex for re-optimization
• Sensitivity analysis for objective and RHS coefficients
• Bland's anti-cycling rule
• Direct minimization and >= / = constraints
• Execution statistics (iterations, pivot counts)

Complexity: O(2^n) worst case, polynomial average

Author

Leandro Rabindranath León

Definition in file Simplex.H.