Find your next solver

Course about advanced modeling for discrete optimization, covering topics such as debugging or predicates

Optimization Expert | Algorithm Design | Operations Research

An arcade-style TSP challenge game written for https://github.com/tunnuz/arcadetsp's 2018 Christmas Party, follow the in-game instructions.

BARON is the industry-leading solver for mixed-integer nonlinear programming (MINLP).

Course about basic modeling for discrete optimization with MiniZinc

Ceres Solver is an open source C++ library for modeling and solving large, complicated optimization problems. It can be used to solve Non-linear Least Squares problems with bounds constraints and general unconstrained optimization problems.

The CG:SHOP Challenge (Computational Geometry: Solving Hard Optimization Problems) is an annual competition dedicated to tackling specific, difficult geometric optimization problems. Originally established as a workshop at Computational Geometry Week (CG Week) in 2019, the Challenge provides a unique platform where the success of proposed solutions is measured based on computational performance on a set of carefully selected benchmark instances. This focus on empirical evaluation marks a shift from traditional computational geometry research, which often emphasizes theoretical approaches.

An Open-Source java library for constraint programming

Chuffed is a state of the art lazy clause solver designed from the ground up with lazy clause generation in mind.

http://clarabel.rs/ is a Rust implementation of an interior point numerical solver for convex optimization problems using a novel homogeneous embedding.

An introduction to algorithms and computational complexity to solve combinatorial optimization problems

CONOPT is a feasible path solver based on advanced active set methods, particularly suited for large and sparse models.

A mathematical optimization solver for large-scale optimization problems. It is independently developed by Cardinal Operations, and it includes high-performance solvers for LP, MIP, SDP, (MI)SOCP, convex (MI)QP, convex (MI)QCP and exponential cone programming.

International conference about Constraint Programming

International conference about the integration of Constraint Programming, Artificial Intelligence and Operations Research

The IBM ILOG CPLEX Optimizer solves integer programming problems, very large[3] linear programming problems using either primal or dual variants of the simplex method or the barrier interior point method, convex and non-convex quadratic programming problems, and convex quadratically constrained problems (solved via second-order cone programming, or SOCP).

CSPLib is a library of test problems for constraint solvers.

CVXPY is an open source Python-embedded modeling language for convex optimization problems. It lets you express your problem in a natural way that follows the math, rather than in the restrictive standard form required by solvers.

Challenges from the Center for Discrete Mathematics and Theoretical Computer Science

The CVXPY Discord community is a group of people who use the CVXPY software to solve convex optimization problems in Python

The HiGHS Discord server.

Journal covering algorithmic and applied areas of discrete mathematics

Course about discrete optimization covering a wide range of optimization techniques such as Constraint Programming, Local Search or Column Generation

The FICO Xpress optimizer is a commercial optimization solver for linear programming (LP), mixed integer linear programming (MILP), convex quadratic programming (QP), convex quadratically constrained quadratic programming (QCQP), second-order cone programming (SOCP) and their mixed integer counterparts. Xpress includes a general purpose non-linear solver, Xpress NonLinear, including a successive linear programming algorithm (SLP, first-order method), and Artelys Knitro (second-order methods).

GCG is a generic decomposition solver for mixed-integer programs (MIPs). It automatically performs a Dantzig-Wolfe reformulation and runs a full-fledged branch-price-and-cut algorithm to solve it to optimality. Alternatively, GCG is able to automatically apply a Benders decomposition.

Gecode is an open source C++ toolkit for developing constraint-based systems and applications. Gecode provides a constraint solver with state-of-the-art performance while being modular and extensible.

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.

Gurobi Optimizer is a prescriptive analytics platform and a decision-making technology developed by Gurobi Optimization, LLC. The Gurobi Optimizer (often referred to as simply, “Gurobi”) is a solver, since it uses mathematical optimization to calculate the answer to a problem.

Blog with news from Gurobi, the company behind one of the most important solvers globally

Use cases from Gurobi

HiGHS is open-source software to solve linear programming (LP), mixed-integer programming (MIP), and convex quadratic programming (QP) models.

To solve a sparse symmetric system of linear equations.

Huub is a Lazy Clause Generation (LCG) solver with a focus on modularity and maintainability in addition to speed. LCG solvers are a class of solvers that can be used to solve decision and optimization problems. They are characterized by their ability to dynamically add new Boolean variables and clauses to a Boolean Satisfiability (SAT) solver during the search process

Optimization software that leverages machine learning to provide unparalleled performance.

Ipopt (Interior Point Optimizer, pronounced "Eye-Pea-Opt") is an open source software package for large-scale nonlinear optimization. It can be used to solve general nonlinear programming problems

Reader in Mathematics at the University of Edinburgh

An innovative constraints programming component able to solve quickly and efficiently a wide range of combinatorial problems relying on an interactive and user-friendly hybrid framework including constraint programming, mixed-integer programming and artificial intelligence.

The most advanced solver for nonlinear optimization.

The 2026 Land-Doig MIP Competition is a computational competition hosted by the 2026 Mixed Integer Programming Workshop, offering an opportunity for teams to showcase their practical and computational prowess and fostering innovation in computational MIP. It is named in honor of Ailsa H. Land and Alison G. Harcourt (née Doig), who proposed the first LP-based branch-and-bound algorithm.

Interactive resources to learn Graph Theory.

LGO is capable of determining high-quality solutions to global optimization problems that have (possibly many) locally optimal solutions. Because LGO makes only limited assumptions as to problem structure and differentiability, it can be applied in a broad range of design and operational applications.

LINGO includes a set of built-in solvers to tackle a wide variety of problems. Unlike many modeling packages, all of the LINGO solvers are directly linked to the modeling environment.

LOQO is a powerful solver for smooth constrained optimization problems, based on interior-point method applied to a sequence of quadratic approximations. Subject to the requirement that the defining functions be smooth (at the points evaluated by the algorithm), LOQO can handle a range of problems: linear or nonlinear, convex or nonconvex, constrained or unconstrained. For convex problems, LOQO finds a globally optimal solution; otherwise, it iterates from the given starting point to find a locally optimal solution.

A Mixed Integer Linear Programming (MILP) solver.

Professor of operations research at RWTH Aachen University.

Creator of Optimization Solvers, CEO at InsideOpt.

MiniZinc is a high-level constraint modelling language that allows you to easily express and solve discrete optimisation problems.

MINOS is an established choice for both linear and nonlinear optimization problems. It incorporates proven methods for large-scale sparse nonlinear constraints, and its methods are especially effective for nonlinear objectives subject to linear and near-linear constraints.

A discussion about books focused on duality theory

Annual challenges from the University of Lehigh

Solves your LPs, QPs, SOCPs, SDPs, and MIPs. Includes interfaces to C, C++, Java, MATLAB, .NET, Python, Julia, Rust and R.

NLopt is a free/open-source library for nonlinear optimization, providing a common interface for a number of different free optimization routines available online as well as original implementations of various other algorithms.

This book offers an up-to-date description of relaxation/approximation and decomposition techniques, demonstrating how their combined use efficiently solves large-scale optimization problems relevant to engineering, particularly in electrical, and industrial engineering, with a focus on energy.

An interesting book about Column Generation to tackle large-scale optimization problems

The OSQP (Operator Splitting Quadratic Program) solver is a numerical optimization package for solving convex quadratic programs.

Challenge from Parameterized Algorithms and Computational Experiments Challenge to bridge the gap between theory and practice of algorithms

The PATH solver for MCP models is a Newton-based solver that combines a number of the most effective variations, extensions, and enhancements of this powerful technique.

PATHNLP is a solver for large nonlinear programming problems that builds on the PATH algorithm, extending it from mixed complementarity problems to general NLPs. PATHNLP is distributed through the GAMS ecosystem.

Instances for Quadratic Assignment Problems.

SBB is a GAMS solver for Mixed Integer Nonlinear Programming (MINLP) models. It is based on a combination of the standard Branch and Bound (B&B) method known from Mixed Integer Linear Programming and some of the standard NLP solvers already supported by GAMS. SBB can use all GAMS NLP solvers as subsolvers but it works best with NLP solvers that can utilize a near optimal point as a starting point like Conopt, Minos, and Snopt.SBB supports all types of discrete variables supported by GAMS, including Binary, Integer, Semicont, Semiint, Sos1, and Sos2.

SCIP is currently one of the fastest non-commercial solvers for mixed integer programming (MIP) and mixed integer nonlinear programming (MINLP). It is also a framework for constraint integer programming and branch-cut-and-price.

SCS (Splitting Conic Solver) is a numerical optimization package for solving large-scale convex quadratic cone problems. The code is freely available on https://github.com/cvxgrp/scs. It solves primal-dual problems.

SHOT (Supporting Hyperplane Optimization Toolkit) is a deterministic solver for mixed-integer nonlinear programming problems (MINLPs). Originally, SHOT was intended for convex MINLP problems only, but now also has functionality to solve nonconvex MINLP problems as a heuristic method without providing any guarantees of global optimality. SHOT can solve certain nonconvex problem types to global optimality as well.

SNDlib is a library of data for Survivable fixed telecommunication Network Design. Its purpose is to provide data about realistic telecommunication networks (including traffic) available to the research community.

A software package for solving large-scale optimization problems (linear and nonlinear programs). It employs a sparse SQP algorithm with limited-memory quasi-Newton approximations to the Hessian of Lagrangian. SNOPT is especially effective for nonlinear problems whose functions and gradients are expensive to evaluate.

Course about solving discrete optimization problems with different techniques: Constraint Programming, Mixed Integer Programming and Local Search

Learn about cutting planes in an adictive way.

Updated fork from OptaPlanner

Mathematical Optimization Researcher, Teacher, and Manager

Another game with map visualizations for the TSP.

Solve the TSP in a visual way from the Productions and Operations Management (Universitat Wein).

TSPLIB is a library of sample instances for the TSP (and related problems) from various sources and of various types.

Uno (Unifying Nonlinear Optimization) is a C++ library that unifies methods for solving nonlinearly constrained optimization problems.

Professor Emeritus, Princeton University/ Co-Founder, Optimal Dynamics, shares knowledge about sequential decision problems.

Z3 is a theorem prover from Microsoft Research.