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# Problem-Based Optimization Setup

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.

## Functions

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 `eqnproblem` Create equation problem `optimproblem` Create optimization problem `optimvar` Create optimization variables `show` Display information about optimization object `showbounds` Display variable bounds `write` Save optimization object description `writebounds` Save description of variable bounds
 `fcn2optimexpr` Convert function to optimization expression `optimconstr` Create empty optimization constraint array `optimeq` Create empty optimization equality array `optimineq` Create empty optimization inequality array `optimexpr` Create empty optimization expression array `show` Display information about optimization object `write` Save optimization object description
 `evaluate` Evaluate optimization expression `findindex` Find numeric index equivalents of named index variables `infeasibility` Constraint violation at a point `prob2struct` Convert optimization problem or equation problem to solver form `show` Display information about optimization object `solve` Solve optimization problem or equation problem `varindex` Map problem variables to solver-based variable index `write` Save optimization object description

## Objects

 `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

## Topics

### Problem-Based Steps

Problem-Based Optimization Workflow

Problem-based steps for solving optimization problems.

Problem-Based Workflow for Solving Equations

Problem-based steps for solving equations.

Optimization Expressions

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.

Write Constraints for Problem-Based Cone Programming

Requirements for `solve` to use `coneprog` for problem solution.

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.

Examine Optimization Solution

How to evaluate the solution and its quality.

### Set Options

Set Options

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.

### Tips for Problem-Based Optimization

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.

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

How to find the values of extra parameters in nonlinear functions created by `prob2struct`.

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.

### Parallel Computing

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 Algorithms

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.

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