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.
There are two approaches to using Optimization Toolbox solvers: problem-based and solver-based. Before you start, choose the approach.
A basic example of solving a nonlinear optimization problem with a nonlinear constraint using the problem-based approach.
Presents an example that minimizes a nonlinear function with a nonlinear constraint.
An example script to modify for using the Optimize Live Editor task.
How to use the Optimize Live Editor task effectively.
Linear problem formulation using the problem-based approach.
Problem formulation using the solver-based approach.
Introduces optimization as a way of finding a set of parameters that can be defined as optimal. These parameters are obtained by minimizing or maximizing an objective function, subject to equality or inequality constraints and/or parameter bounds.
Descriptions of optimization solvers.
Explains why solvers might not find the smallest minimum.