# Problem-Based Nonlinear Optimization

Solve nonlinear optimization problems in serial or parallel using the problem-based approach

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.

Formulate your objective and nonlinear constraint functions as expressions in optimization variables, or convert MATLAB® functions using `fcn2optimexpr`. For problem setup, see Problem-Based Optimization Setup.

## Functions

 `evaluate` Evaluate optimization expression `fcn2optimexpr` Convert function to optimization expression `infeasibility` Constraint violation at a point `optimproblem` Create optimization problem `optimvar` Create optimization variables `prob2struct` Convert optimization problem or equation problem to solver form `solve` Solve optimization problem or equation problem

## Topics

### Unconstrained Problem-Based Applications

Rational Objective Function, Problem-Based

This example shows how to create a rational objective function using optimization variables and solve the resulting unconstrained problem.

### Constrained Problem-Based Applications

Solve Constrained Nonlinear Optimization, Problem-Based

This example shows how to solve a constrained nonlinear problem based on optimization expressions. The example also shows how to convert a nonlinear function to an optimization expression.

Convert Nonlinear Function to Optimization Expression

Convert nonlinear functions, whether expressed as function files or anonymous functions, by using `fcn2optimexpr`.

Constrained Electrostatic Nonlinear Optimization, Problem-Based

Shows how to define objective and constraint functions for a structured nonlinear optimization in the problem-based approach.

Problem-Based Nonlinear Minimization with Linear Constraints

Shows how to use optimization variables to create linear constraints, and `fcn2optimexpr` to convert a function to an optimization expression.

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`.

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.

Solve Nonlinear Feasibility Problem, Problem-Based

Solve a feasibility problem, which is a problem with constraints only.

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

Improving Performance with Parallel Computing

Investigate factors for speeding optimizations.

### Simulation or ODE

Optimizing a Simulation or Ordinary Differential Equation

Special considerations in optimizing simulations, black-box objective functions, or ODEs.

### Algorithms and Other Theory

Unconstrained Nonlinear Optimization Algorithms

Minimizing a single objective function in n dimensions without constraints.

Constrained Nonlinear Optimization Algorithms

Minimizing a single objective function in n dimensions with various types of constraints.

fminsearch Algorithm

Steps that `fminsearch` takes to minimize a function.

Optimization Options Reference

Explore optimization options.

Local vs. Global Optima

Explains why solvers might not find the smallest minimum.

Bibliography

Lists published materials that support concepts implemented in the solver algorithms.