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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, and solve the problem using `solve`. For the problem-based steps to take, see Problem-Based Workflow.

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

Note: If you have a nonlinear function that is not a polynomial or rational expression, convert it to an optimization expression by using `fcn2optimexpr`. See Convert Nonlinear Function to Optimization Expression.

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.

## Functions

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 `optimproblem` Create optimization problem `optimvar` Create optimization variables `showbounds` Display variable bounds `showproblem` Display optimization problem `showvar` Display optimization variable `writebounds` Save description of variable bounds `writeproblem` Save optimization problem description `writevar` Save optimization variable description
 `fcn2optimexpr` Convert function to optimization expression `optimconstr` Create empty optimization constraint array `optimexpr` Create empty optimization expression array `showconstr` Display optimization constraint `showexpr` Display optimization expression `writeconstr` Save optimization constraint description `writeexpr` Save optimization expression description
 `evaluate` Evaluate optimization expression `findindex` Find numeric index equivalents of named index variables `infeasibility` Constraint violation at a point `prob2struct` Convert optimization problem to solver form `solve` Solve optimization problem `varindex` Map problem variables to solver-based variable index

## Objects

 `OptimizationConstraint` Optimization constraints `OptimizationExpression` Objective function or constraints `OptimizationProblem` Optimization problem `OptimizationVariable` Variable for optimization

## Topics

### Problem-Based Steps

Problem-Based Workflow

Problem-based steps for solving optimization problems.

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.

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.

### Parallel Computing

What Is Parallel Computing in Optimization Toolbox?

Using multiple processors for optimization.

Using Parallel Computing in Optimization Toolbox

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

Considerations for speeding optimizations.

### Problem-Based Algorithms

Problem-Based Optimization Algorithms

How the optimization functions and objects solve optimization problems.

Supported Operations on Optimization Variables and Expressions

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

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