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Integer programming is NP-complete. In particular, the special case of 0–1 integer linear programming, in which unknowns are binary, and only the restrictions must be satisfied, is one of Karp's 21 NP-complete problems. [1] If some decision variables are not discrete, the problem is known as a mixed-integer programming problem. [2]
MPS (Mathematical Programming System) is a file format for presenting and archiving linear programming (LP) and mixed integer programming problems. Overview [ edit ]
HiGHS is open-source software to solve linear programming (LP), mixed-integer programming (MIP), and convex quadratic programming (QP) models. [1] Written in C++ and published under an MIT license, HiGHS provides programming interfaces to C, Python, Julia, Rust, R, JavaScript, Fortran, and C#. It has no external dependencies.
Artelys Knitro – large scale nonlinear optimization for continuous and mixed-integer programming. ASTOS – AeroSpace Trajectory optimization Software for launch, re-entry, and generic aerospace problems. BARON – optimization of algebraic nonlinear and mixed-integer nonlinear problems.
Single- or multi-process optimization over networks (SYMPHONY) is an open source branch and cut framework for solving mixed integer programs (MIPs) over heterogeneous networks. [9] It can use CLP, CPLEX, XPRESS or other linear programming solvers to solve the underlying linear programs.
Google OR-Tools is a free and open-source software suite developed by Google for solving linear programming (LP), mixed integer programming (MIP), constraint programming (CP), vehicle routing (VRP), and related optimization problems. [3] OR-Tools is a set of components written in C++ but provides wrappers for Java, .NET and Python.
Convex Over and Under ENvelopes for Nonlinear Estimation (Couenne) is an open-source library for solving global optimization problems, also termed mixed integer nonlinear optimization problems. [1] A global optimization problem requires to minimize a function, called objective function, subject to a set of constraints. Both the objective ...
MOSEK is a software package for the solution of linear, mixed-integer linear, quadratic, mixed-integer quadratic, quadratically constrained, conic and convex nonlinear mathematical optimization problems. The applicability of the solver varies widely and is commonly used for solving problems in areas such as engineering, finance and computer ...