Solve linear, quadratic, integer, and nonlinear optimization problems

Optimization Toolbox™ provides functions for finding parameters that minimize or maximize objectives while satisfying constraints. The toolbox includes solvers for linear programming (LP), mixed-integer linear programming (MILP), quadratic programming (QP), nonlinear programming (NLP), constrained linear least squares, nonlinear least squares, and nonlinear equations. You can define your optimization problem with functions and matrices or by specifying variable expressions that reflect the underlying mathematics.

You can use the toolbox solvers to find optimal solutions to continuous and discrete problems, perform tradeoff analyses, and incorporate optimization methods into algorithms and applications. The toolbox lets you perform design optimization tasks, including parameter estimation, component selection, and parameter tuning. It can be used to find optimal solutions in applications such as portfolio optimization, resource allocation, and production planning and scheduling.


Defining and Solving Optimization Problems

Find a set of design parameters or decisions that give the best possible result.

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Nonlinear Optimization

Solve nonlinear programming problems.

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Linear and Quadratic Programming

Solve large-scale linear and quadratic optimization problems.

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Mixed-Integer Linear Programming

Solve mixed-integer linear optimization problems.

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Multiobjective Optimization

Solve optimization problems with multiple objectives.

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Nonlinear Least Squares, Data Fitting, and Nonlinear Equations

Solve linear and nonlinear least-squares problems, data fitting problems, and nonlinear equations.

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Parallel Computing

Accelerate optimization solvers with parallel computing.

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Product Resources

Discover more about Optimization Toolbox by exploring these resources.


Explore documentation for Optimization Toolbox functions and features, including release notes and examples.


Browse the list of available Optimization Toolbox functions.

Technical Articles

View articles that demonstrate technical advantages of using Optimization Toolbox.

User Stories

Read how Optimization Toolbox is accelerating research and development in your industry.

Community and Support

Find answers to questions and explore troubleshooting resources.

Product Requirements

View product requirements for the latest release of Optimization Toolbox.

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Optimization Toolbox requires: MATLAB

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