# Documentation

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# Constrained Optimization

Solve constrained minimization and semi-infinite programming problems in serial or parallel

## Functions

 `fminbnd` Find minimum of single-variable function on fixed interval `fmincon` Find minimum of constrained nonlinear multivariable function `fseminf` Find minimum of semi-infinitely constrained multivariable nonlinear function

## Topics

### Standard Constraints

Optimization App with the fmincon Solver

Example of nonlinear programming with constraints using the Optimization app.

Nonlinear Inequality Constraints

Example of nonlinear programming with nonlinear inequality constraints.

Example of nonlinear programming with derivative information.

fmincon Interior-Point Algorithm with Analytic Hessian

Example of nonlinear programming with all derivative information.

This example shows how to solve an optimization problem that has a linear or quadratic objective and quadratic inequality constraints.

Nonlinear Equality and Inequality Constraints

Nonlinear programming with both types of nonlinear constraints.

Minimization with Bound Constraints and Banded Preconditioner

Example showing efficiency gains possible with structured nonlinear problems.

Minimization with Linear Equality Constraints

Example showing nonlinear programming with only linear equality constraints.

Minimization with Dense Structured Hessian, Linear Equalities

Example showing how to save memory in nonlinear programming with a structured Hessian and only linear equality constraints or only bounds.

Symbolic Math Toolbox Calculates Gradients and Hessians

Example showing how to calculate derivatives symbolically for optimization solvers.

### Semi-Infinite Constraints

One-Dimensional Semi-Infinite Constraints

Example showing how to use one-dimensional semi-infinite constraints in nonlinear programming.

Two-Dimensional Semi-Infinite Constraint

Example showing how to use two-dimensional semi-infinite constraints in nonlinear programming.

### Parallel Computing

What Is Parallel Computing in Optimization Toolbox?

Using multiple processors for optimization.

Using Parallel Computing in Optimization Toolbox

Improving Performance with Parallel Computing

Considerations for speeding optimizations.

### Simulation or ODE

Optimizing a Simulation or Ordinary Differential Equation

Special considerations in optimizing simulations, black-box objective functions, or ODEs.

### Algorithms and Other Theory

Constrained Nonlinear Optimization Algorithms

Minimizing a single objective function in n dimensions with various types of constraints.

Optimization Options Reference

Describes optimization options.

Local vs. Global Optima

Explains why solvers might not find the smallest minimum.

Bibliography

Lists published materials that support concepts implemented in the solver algorithms.