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基于问题的非线性优化

使用基于问题的方法以串行或并行方式求解非线性优化问题

在开始求解优化问题之前,您必须选择合适的方法:基于问题或基于求解器。有关详细信息,请参阅首先选择基于问题或基于求解器的方法

将您的目标和非线性约束函数表示为使用优化变量的表达式,或使用 fcn2optimexpr 转换 MATLAB® 函数。有关问题设置,请参阅基于问题的优化设置

函数

evaluate计算优化表达式
fcn2optimexpr将函数转换为优化表达式
infeasibility一个点处的约束违反度
optimproblem创建优化问题
optimvar创建优化变量
prob2struct将优化问题或方程问题转换为求解器形式
solve求解优化问题或方程问题

主题

基于无约束问题的应用

Rational Objective Function, Problem-Based

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

基于有约束问题的应用

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

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.

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.

并行计算

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.

仿真或 ODE

优化仿真或常微分方程

优化仿真、黑盒目标函数或 ODE 时的特殊注意事项。

算法和其他理论

无约束非线性优化算法

在无约束的情况下,在 n 个维度中最小化单目标函数。

约束非线性优化算法

在有各种约束的情况下,在 n 个维度中最小化单目标函数。

fminsearch Algorithm

Steps that fminsearch takes to minimize a function.

优化选项参考

了解优化选项。

局部最优与全局最优

解释为什么求解器可能找不到最小的最小值。

参考书目

这里列出的资料支持求解器算法中实现的概念并均已发表。