Optimization Toolbox
Solve linear, quadratic, conic, integer, and nonlinear optimization problems
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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), second-order cone programming (SOCP), 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 automatic differentiation of objective and constraint functions for faster and more accurate solutions.
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 enables you to find optimal solutions in applications such as portfolio optimization, energy management and trading, and production planning.
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Connect AI Agents to Optimization Toolbox
Bring domain-specific capabilities to your agentic AI workflow.
Getting Started with Optimization
Start with Optimization Onramp training or the Optimize Live Editor live task for hands-on practice to build core optimization skills in MATLAB. Review example problems to learn new skills and best practices in optimization.
Design Exploration with Optimization
Explore unconventional designs to better achieve your design objectives. Optimization Explorer extends this feature for multisolver exploration and analysis.
Schedule and Resource Optimization
Use MILP solvers in Optimization Toolbox to solve resource allocation and scheduling problems. Examples include electric grid load balancing, manufacturing process optimization, and mission engineering.
Optimization with AI Agents
Use MATLAB Copilot or agentic coding tools connected through MATLAB Agentic Toolkit and the MATLAB MCP Server to formulate optimization problems, evaluate tradeoffs, and generate optimization workflows.
Automatic Solver Selection
Use the problem-based approach to define and solve optimization problems in natural math form without needing to specify which solver to use.
Configurable Solvers for Performance
Use the solver-based approach to configure any of the supported Optimization solvers (see solver list). Use the Optimization Explorer app to compare the performance of different solvers and solver options for your problem.
Optimization with AI Models
Use AI surrogate or reduced order models (ROMs) with Optimization Toolbox to improve design exploration speed in CFD and FEA workflows. These models preserve the original simulation fidelity for final validation.
Balancing Competing Objectives
Balance multiple objectives under constraints using fgoalattain and fminimax. For additional Pareto-front solvers like paretosearch and gamultiobj, add Global Optimization Toolbox.
Scale and Deploy Optimization
Build optimization-based decision support and design tools, integrate with enterprise systems, and deploy optimization algorithms on embedded systems.
Product Resources:
“MATLAB has helped accelerate our R&D and deployment with its robust numerical algorithms, extensive visualization and analytics tools, reliable optimization routines, support for object-oriented programming, and ability to run in the cloud with our production Java applications.”
Optimization Toolbox FAQs
Optimization Toolbox is a MATLAB product that 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), second-order cone programming (SOCP), nonlinear programming (NLP), constrained linear least squares, nonlinear least squares, and nonlinear equations.
You can define problems using variable expressions that reflect the underlying mathematics (problem-based approach) or with functions and matrices (solver-based approach).
Automatic differentiation of objective and constraint functions enables faster and more accurate solutions to optimization problems.
The toolbox enables portfolio optimization, energy management and trading, production planning, parameter estimation, component selection, and parameter tuning.
Yes, you can build optimization-based decision support and design tools, integrate with enterprise systems, and deploy optimization algorithms to embedded systems.
Yes, the toolbox can solve optimization problems that have multiple objective functions subject to a set of constraints.
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