# Get Started with Problem-Based Optimization and Equations

To solve a problem using the problem-based approach, perform these steps.

Create an optimization problem using

`optimproblem`

or an equation-solving problem using`eqnproblem`

.Create optimization variables using

`optimvar`

.Create expressions using the optimization variables representing the objective, constraints, or equations. Place the expressions into the problem using dot notation, such as

prob.Objective = expression1; probl.Constraints.ineq = ineq1;

For nonlinear problems, create an initial point

`x0`

as a structure, with the names of the optimization variables as the fields.Solve the problem by calling

`solve`

.

To improve your setup, increase performance, or learn details about problem-based setup, see Improve Problem-Based Organization and Performance.

For parallel computing in Optimization Toolbox™, see the last section; for parallel computing in Global Optimization Toolbox, see How to Use Parallel Processing in Global Optimization Toolbox (Global Optimization Toolbox).

## Functions

## 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 |

`OptimizationValues` | Values for optimization problems (Since R2022a) |

`OptimizationVariable` | Variable for optimization |

## Live Editor Tasks

Optimize | Optimize or solve equations in the Live Editor (Since R2020b) |

## Topics

### Problem-Based Procedures

**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.**Optimization Expressions**

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.**Review or Modify Optimization Problems**

Review or modify problem elements such as variables and constraints.**Examine Optimization Solution**

Evaluate the solution and its quality.

### Limitations

**Variables with Duplicate Names Disallowed**

Learn how to solve a problem that has two optimization variables with the same name.**Expression Contains Inf or NaN**

Optimization expressions containing`Inf`

or`NaN`

cannot be displayed, and can cause unexpected results.

### Tune and Monitor Solution Process

**Set Optimization Options, Problem-Based**

How to set and change optimization options in the problem-based approach.**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.

### Algorithms

**Problem-Based Optimization Algorithms**

Learn how the optimization functions and objects solve optimization problems.**fcn2optimexpr Algorithm Description**

How`fcn2optimexpr`

works.**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.

### Parallel Computing in Optimization Toolbox

**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.