Formulate optimization problems using variables and expressions, solve in
serial or parallel

In problem-based optimization you create optimization variables,
expressions in these variables that represent the objective and constraints
or that represent equations, and solve the problem using `solve`

. For the problem-based steps to take for optimization
problems, see Problem-Based Optimization Workflow. For
equation-solving, see Problem-Based Workflow for Solving Equations.

Before you begin to solve an optimization problem, you must choose the appropriate approach: problem-based or solver-based. For details, see First Choose Problem-Based or Solver-Based Approach.

**Note:** If you have a nonlinear function
that is not composed of polynomials, rational expressions, and elementary
functions such as `exp`

, then convert the function to an
optimization expression by using `fcn2optimexpr`

. See Convert Nonlinear Function to Optimization Expression and
Supported Operations on Optimization Variables and Expressions.

For a basic nonlinear optimization example, see Solve a Constrained Nonlinear Problem, Problem-Based. For a basic mixed-integer linear programming example, see Mixed-Integer Linear Programming Basics: Problem-Based. For a basic equation-solving example, see Solve Nonlinear System of Equations, Problem-Based.

`EquationProblem` | System of nonlinear equations |

`OptimizationConstraint` | Optimization constraints |

`OptimizationEquality` | Equalities and equality constraints |

`OptimizationExpression` | Arithmetic or functional expression in terms of optimization variables |

`OptimizationInequality` | Inequality constraints |

`OptimizationProblem` | Optimization problem |

`OptimizationVariable` | Variable for optimization |

**Problem-Based Optimization Workflow**

Problem-based steps for solving optimization problems.

**Problem-Based Workflow for Solving Equations**

Problem-based steps for solving equations.

Expressions define both objective and constraints.

**Pass Extra Parameters in Problem-Based Approach**

Pass extra parameters, data, or fixed variables in the problem-based approach.

**Write Objective Function for Problem-Based Least Squares**

Syntax rules for problem-based least squares.

**Named Index for Optimization Variables**

How to create and work with named indices for variables.

**Review or Modify Optimization Problems**

Shows how to review or modify problem elements such as variables and constraints.

How to evaluate the solution and its quality.

Set optimization options

**Output Function for Problem-Based Optimization**

Shows how to use an output function in the problem-based approach to record iteration history and to make a custom plot.

**Create Efficient Optimization Problems**

Tips for obtaining a faster or more accurate solution when there are integer constraints, and for avoiding loops in problem creation.

**Separate Optimization Model from Data**

To create reusable, scalable problems, separate the model from the data.

**Variables with Duplicate Names Disallowed**

Solution to the problem of two optimization variables with the same name.

**Create Initial Point for Optimization with Named Index Variables**

This example shows how to create initial points for `solve`

when you have named index variables by using the `findindex`

function.

**Expression Contains Inf or NaN**

Optimization expressions containing `Inf`

or
`NaN`

cannot be displayed, and can cause unexpected
results.

**Objective and Constraints Having a Common Function in Serial or Parallel, Problem-Based**

Save time when your objective and nonlinear constraint functions share common computations in the problem-based approach.

**Effect of Automatic Differentiation in Problem-Based Optimization**

Automatic differentiation lowers the number of function evaluations for solving a problem.

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

Use multiple processors for optimization.

**Using Parallel Computing in Optimization Toolbox**

Perform gradient estimation in parallel.

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

Example showing the effectiveness of parallel computing
in two solvers: `fmincon`

and `ga`

.

**Improving Performance with Parallel Computing**

Investigate factors for speeding optimizations.

**Problem-Based Optimization Algorithms**

How the optimization functions and objects solve optimization problems.

**Automatic Differentiation Background**

Learn how automatic differentiation works.

**Supported Operations on Optimization Variables and Expressions**

Lists all available mathematical and indexing operations on optimization variables and expressions.