Problem-Based Nonlinear Optimization
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.
|Evaluate optimization expression
|Convert function to optimization expression (Since R2019a)
|Constraint violation at a point
|Create optimization problem
|Create optimization variables
|Convert optimization problem or equation problem to solver form
|Solve optimization problem or equation problem
Live Editor Tasks
|Optimize or solve equations in the Live Editor (Since R2020b)
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
- 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
fcn2optimexprto 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
- 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
- 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.
- 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
fminsearchtakes 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.