Find your next solver

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

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

Optimization Expert | Algorithm Design | Operations Research

Prof Marco Lubbecke talks about optimization in a TED Talk.

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.

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.

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

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

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

The most advanced solver for nonlinear optimization.

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.

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.

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

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.

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.

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.

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.

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

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.