Find your next solver

Learn more about how AI is changing businesses and how you can leverage it: Insights, tools, tips, and expert voices

Blog with news from the Operations Research and Optimization group at Amazon

Prof Marco Lubbecke talks about optimization in a TED Talk.

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

Learn supply chain principles through a visual simulation.

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.

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.

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

Customer success stories from Coupa including optimization problems

International conference about Constraint Programming

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

CSPLib is a library of test problems for constraint solvers.

Achieve world-record speed on large-scale problems with millions of constraints and variables—saving time and reducing costs.

A game to better understand how CVRP works.

Instances for the CVRP challenge.

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.

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

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.

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

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

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.

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.

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.

Assistant Professor of Transportation Engineering @ York University | Director of Interactive-OR | Amazon Visiting Academic @ Amazon

Creator of Optimization Solvers, CEO at InsideOpt.

Teaching and writing about all things AI, operations, and his startup experience.

Practical AI for business, my experience starting and selling a company, and other content.

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.

An extensible framework for solving discrete optimization problems using a combination of Mixed-Integer Linear Programming (MIP) and Machine Learning (ML). MIPLearn uses ML methods to automatically identify patterns in previously solved instances of the problem, then uses these patterns to accelerate the performance of conventional state-of-the-art MIP solvers such as CPLEX, Gurobi or XPRESS.

Thought leadership from the MIT Center for Transportation & Logistics.

Introduction to the field of mathematical optimization.

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.

Case studies from Optimal Dynamics

Customer success stories from ORTEC

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

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.

President of Optisol, Scheduling Specialist for High-Variety, Order-Driven Production and Resource-Constrained Projects.

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.

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.

Updated fork from OptaPlanner

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

Vehicle Routing and Logistics work group from EURO

This web is dedicated to the study of VRP; we have compiled here a great deal of information about it for public access: technical reports, many different variants of the problem, alternative algorithms and techniques for solving it, some well-known instances of the problem, the best-so-far solutions for those instances, bibliography, related links…

Z3 is a theorem prover from Microsoft Research.