Solve nonlinear minimization and semi-infinite programming problems in
serial or parallel using the solver-based approach

See First Choose Problem-Based or Solver-Based Approach for choosing between problem-based optimization and solver-based optimization.

For problem setup, see Solver-Based Optimization Problem Setup.

`fminbnd` | Find minimum of single-variable function on fixed interval |

`fmincon` | Find minimum of constrained nonlinear multivariable function |

`fminsearch` | Find minimum of unconstrained multivariable function using derivative-free method |

`fminunc` | Find minimum of unconstrained multivariable function |

`fseminf` | Find minimum of semi-infinitely constrained multivariable nonlinear function |

Shows how to solve for the minimum of Rosenbrock's function using different solvers, with or without gradients.

**fminunc Unconstrained Minimization**

Example of unconstrained nonlinear programming.

**Minimization with Gradient and Hessian**

Example of unconstrained nonlinear programming including derivatives.

**Minimization with Gradient and Hessian Sparsity Pattern**

Example of nonlinear programming using some derivative information.

**Tutorial for the Optimization Toolbox™**

Tutorial example showing how to solve nonlinear problems and pass extra parameters.

**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.

**Nonlinear Constraints with Gradients**

Example of nonlinear programming with derivative information.

**fmincon Interior-Point Algorithm with Analytic Hessian**

Example of nonlinear programming with all derivative information.

**Linear or Quadratic Objective with Quadratic Constraints**

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.

**How to Use All Types of Constraints**

Example showing all 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.

**Using Symbolic Mathematics with Optimization Toolbox™ Solvers**

Use Symbolic Math Toolbox™ to generate gradients and Hessians.

**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.

**Analyzing the Effect of Uncertainty Using Semi-Infinite Programming**

This example shows how to use semi-infinite programming to investigate the effect of uncertainty in the model parameters of an optimization problem.

**What Is Parallel Computing in Optimization Toolbox?**

Using multiple processors for optimization.

**Using Parallel Computing in Optimization Toolbox**

Automatic gradient estimation in parallel.

**Improving Performance with Parallel Computing**

Considerations for speeding optimizations.

**Minimizing an Expensive Optimization Problem Using Parallel Computing Toolbox™**

Example showing how to use parallel computing in both Global Optimization Toolbox and Optimization Toolbox™ solvers.

**Optimizing a Simulation or Ordinary Differential Equation**

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

**Unconstrained Nonlinear Optimization Algorithms**

Minimizing a single objective function in *n* dimensions
without constraints.

**Constrained Nonlinear Optimization Algorithms**

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

Steps that `fminsearch`

takes to
minimize a function.

**Optimization Options Reference**

Describes optimization options.

Explains why solvers might not find the smallest minimum.

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