Linear Solvers – handling linear optimization problems in both continuous and integer variables. These are adequate for modest problems.
Cbc (Coin-or branch and cut) is an open-source mixed integer programming solver written in C++. It can be used as a callable library or using a stand-alone executable. It can be called through AMPL (natively), GAMS (using the links provided by the Optimization Services and GAMSlinks projects), MPL (through the CoinMP project), AIMMS (through the AIMMSlinks project), PuLP, CMPL, OpenSolver for Excel, orJuMP.
GLPK (GNU Linear Programming Kit) package is intended for solving large-scale linear programming (LP), mixed integer programming (MIP), and other related problems. It is a set of routines written in ANSI C and organized in the form of a callable library. GLPK supports the GNU MathProg modeling language, which is a subset of the AMPL language.
lpsolve – Mixed Integer Linear Programming (MILP) solver lp_solve solves pure linear, (mixed) integer/binary, semi-cont and special ordered sets (SOS) models.lp_solve is written in ANSI C and can be compiled on many different platforms like Linux and WINDOWS
Nonlinear Solvers – solve problems involving smooth nonlinear functions such as powers, logs and ratios.Work well with smaller problems.
Ipopt (Interior Point OPTimizer, pronounced eye-pea-Opt) is a software package for large-scale nonlinear optimization. It is designed to find (local) solutions of mathematical optimization problems.
Bonmin (Basic Open-source Nonlinear Mixed INteger programming) is an experimental open-source C++ code for solving general MINLP (Mixed Integer NonLinear Programming) problems.
Couenne (Convex Over and Under ENvelopes for Nonlinear Estimation) is a branch&bound algorithm to solve Mixed-Integer Nonlinear Programming (MINLP) problems.
MIDACO is a solver for general optimization problems. MIDACO can be applied on continuous (NLP), discrete/integer (IP) and mixed integer (MINLP) problems. Problems may be restricted to equality and/or inequality constraints. MIDACO is suitable for problems with up to several hundreds to some thousands optimization variables. MIDACO implements a derivative-free, heuristic algorithm that treats the problem as black-box which may contain critical function properties such as non-convexity, discontinuities or stochastic noise. For cpu-time expensive applications, MIDACO offers an efficientparallelization strategy. The software is available in several programming languages, such as Excel, Matlab, Python, R, C/C++ and Fortran.
The MOSEK Optimization Software is designed to solve large-scale mathematical optimization problems. MOSEK provides specialized solvers for linear programming, mixed integer programming and many types of nonlinear convex optimization problems. The state-of-art conic quadratic (aka. SOCP) optimizer in MOSEK makes it ideal for financial applications such as portfolio optimization.
Constraint Programming Solvers – for constraint programming problems, often in discrete variables.
Gecode is a toolkit for developing constraint-based systems and applications. Gecode provides a constraint solver with state-of-the-art performance while being modular and extensible.
JaCoP is a Java Constraint Programming solver. It provides a significant number of (global) constraints to facilitate efficient modeling. It also provides modular design of search to help user tailor search to specific characteristics of problem being addressed.