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 or objectives and constraints in problem
`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

Live Editor Tasks

Optimize

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

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 Using Optimization Variables
Define objective and constraint functions for a structured nonlinear optimization in the problem-based approach.
Discretized Optimal Trajectory, Problem-Based
This example shows how to solve a discretized optimal trajectory problem using 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
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 the 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.
Feasibility Using Problem-Based Optimize Live Editor Task
Solve a nonlinear feasibility problem using the problem-based Optimize Live Editor task and several solvers.
Obtain Solution Using Feasibility Mode
Solve a problem with difficult constraints using fmincon feasibility mode.
Monitor Solution Process with optimplot
View details of the optimization solution process using optimplot.
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.
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.
Smooth Formulations of Nonsmooth Functions
Reformulate some nonsmooth functions as smooth functions by using auxiliary variables.
Optimization Bibliography
Lists published materials that support concepts implemented in the optimization solver algorithms.

Related Information

Problem-Based Nonlinear Programming