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 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. For an example using the Optimize Live Editor task, see Get Started with Problem-Based Optimize Live Editor Task.

Functions

expand all

Create Variables and Problem

`eqnproblem`	Create equation problem
`optimproblem`	Create optimization problem
`optimvalues`	Create values for 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

Expressions, Constraints, and Equations

`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

Solve and Analyze

`evaluate`	Evaluate optimization expression
`findindex`	Find numeric index equivalents of named index variables
`infeasibility`	Constraint violation at a point
`paretoplot`	Pareto plot of multiobjective values
`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
`OptimizationValues`	Values for optimization problems
`OptimizationVariable`	Variable for optimization

Live Editor Tasks

Optimize

Optimize or solve equations in the Live Editor

Topics

Problem-Based Steps

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.
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.
Examine Optimization Solution
Evaluate the solution and its quality.

Set Options

Set Options
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.

Tips for Problem-Based Optimization

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.
Initialize Optimization Expressions
How initialize optimization expressions in functions, and how to recognize that you need to initialize them.
Use Problem-Based Optimize Live Editor Task Effectively
How to use and understand the problem-based Optimize Live Editor task.
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.

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
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.