Main Content

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 for 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**

Learn the problem-based steps for solving optimization problems.

**Problem-Based Workflow for Solving Equations**

Learn the problem-based steps for solving equations.

Define expressions for both the 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.

**Write Constraints for Problem-Based Cone Programming**

Requirements for `solve`

to use `coneprog`

for problem solution.

**Named Index for Optimization Variables**

Create and work with named indices for variables.

**Review or Modify Optimization Problems**

Review or modify problem elements such as variables and constraints.

Evaluate the solution and its quality.

Set optimization options

**Output Function for Problem-Based Optimization**

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

**Create Efficient Optimization Problems**

Obtain a faster or more accurate solution when the problem has integer constraints, and avoid loops when creating a problem.

**Separate Optimization Model from Data**

Create reusable, scalable problems by separating the model from the data.

**Variables with Duplicate Names Disallowed**

Learn how to solve a problem that has two optimization variables with the same name.

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

Create initial points for `solve`

when the problem has 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 the 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.

**Supply Derivatives in Problem-Based Workflow**

How to include derivative information in problem-based optimization when automatic derivatives do not apply.

**Obtain Generated Function Details**

Find the values of extra parameters in nonlinear functions created by
`prob2struct`

.

**Integer Constraints in Nonlinear Problem-Based Optimization**

Learn how the problem-based optimization functions
`prob2struct`

and `solve`

handle integer
constraints.

**Output Function for Problem-Based Optimization**

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

**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**

Learn how the optimization functions and objects solve optimization problems.

**Automatic Differentiation Background**

Learn how automatic differentiation works.

**Supported Operations for Optimization Variables and Expressions**

Explore the supported mathematical and indexing operations for optimization variables and expressions.