Problem-Based Global Optimization Setup

Create optimization variables, create problem with objective and constraints, call solve

Global Optimization Toolbox has two approaches for optimization: problem-based and solver-based. See Decide Between Problem-Based and Solver-Based Approach. In problem-based optimization, you create symbolic-style optimization variables. Then you create expressions in these variables that represent the objective and constraints. Finally, solve the problem using solve. For details, see Problem-Based Optimization Workflow.

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 example, see Compare Several Global Solvers, Problem-Based.

Functions

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Create Variables and Problem

`optimproblem`	Create optimization problem
`optimvalues`	Create values for optimization problem (Since R2022a)
`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

Create 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 or objectives and constraints in problem
`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

`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

Topics

Problem-Based Steps

Problem-Based Optimization Workflow
Learn the problem-based steps for solving optimization problems.
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.
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.

Steps for Global Solvers

Decide Between Problem-Based and Solver-Based Approach
Explore considerations for problem-based and solver-based optimization with Global Optimization Toolbox solvers.
Global Optimization Toolbox Default Solvers and Problem Types
Identify the types of problems you can solve in the problem-based approach and their associated default solvers.
Initial Points for Global Optimization Toolbox Solvers
Specify initial points for Global Optimization Toolbox solvers in the problem-based approach.
Integer Constraints in Nonlinear Problem-Based Optimization
Learn how the problem-based optimization functions prob2struct and solve handle integer constraints.

Set Global Optimization Options

Set Problem-Based Optimization Options for Global Optimization Toolbox Solvers
How to set and change optimization options in the problem-based approach for Global Optimization Toolbox.
Set Options in Problem-Based Approach Using varindex
To set options in some contexts, map problem-based variables to solver-based using varindex.
Pattern Search Options
Explore the options for pattern search.
Genetic Algorithm Options
Explore the options for the genetic algorithm.
Particle Swarm Options
Explore the options for particle swarm.
Surrogate Optimization Options
Explore the options for surrogate optimization, including algorithm control, stopping criteria, command-line display, and output and plot functions.
Simulated Annealing Options
Explore the options for simulated annealing.

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.
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.
Obtain Generated Function Details
Find the values of extra parameters in nonlinear functions created by prob2struct.
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

How Solvers Compute in Parallel
Learn how solvers distribute work for parallel computing.
How to Use Parallel Processing in Global Optimization Toolbox
Direct a solver or hybrid function to use multiple processes.
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.
Supported Operations for Optimization Variables and Expressions
Explore the supported mathematical and indexing operations for optimization variables and expressions.