Matlab fmincon函数用法

全栈程序员-站长 • 2022年6月22日下午11:16 • 未分类 • 阅读 55

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原文地址：长笛人倚楼Gloria

这个函数在之前优化工具箱一文中已经介绍过，由于其应用广泛，所以这里通过实例单独整理一下其用法。

一、基本介绍

求解问题的标准型为

min F(X)

s.t

AX <= b

AeqX = beq

G(x) <= 0

Ceq(X) = 0

VLB <= X <= VUB

其中X为n维变元向量，G(x)与Ceq(X)均为非线性函数组成的向量，其它变量的含义与线性规划，二次规划中相同，用Matlab求解上述问题，基本步骤分为三步：

1. 首先建立M文件fun.m定义目标函数F(X)：

function f = fun(X);

f = F(X)

2. 若约束条件中有非线性约束：G(x) <= 0 或 Ceq(x) = 0，则建立M文件nonlcon.m定义函数G(X)和Ceq(X);

function [G, Ceq] = nonlcon(X)

G = …

Ceq = …

3. 建立主程序，非线性规划求解的函数时fmincon，命令的基本格式如下：

function ex131101

x0 = [1; 1];

A = [2, 3; 1, 4];

b = [6, 5];

Aeq = [];

beq = [];

VLB = [0; 0];

VUB = [];

[x, fval] = fmincon(@fun3, x0, A, b, Aeq, beq, VLB, VUB)

function f = fun3(x)

f = -x(1) – 2*x(2) + (1/2)*x(1)^2 + (1/2)*x(2)^2;

2. 第二种方法，通过函数设置边界

例2： min f(x) = exp(x1) * (4*x1^2 + 2*x2^2 + 4*x1*x2 + 2*x2 + 1)

x1 + x2 = 0

1.5 + x1 * x2 – x1 – x2
<= 0

-x1*x2 – 10 <= 0

function youh3

clc;

x0 = [-1, 1];

A = [];b = [];

Aeq = []; beq = [];

vlb = []; vub = [];

[x, fval] = fmincon(@fun4, x0, A, b, Aeq, beq, vlb, vub, @mycon)

function f = fun4(x);

f = exp(x(1)) * (4*x(1)^2 + 2*x(2)^2 + 4*x(1)*x(2) + 2*x(2) + 1);

function [g, ceq] = mycon(x)

g = [1.5 + x(1)*x(2) – x(1) – x(2); -x(1)*x(2) – 10];

ceq = [x(1) + x(2)];

3. 进阶用法，增加梯度以及传递参数

这里用无约束优化函数fminunc做示例，对于fmincon方法相同，只需将边界项设为空即可。

（1）定义目标函数

function [J, grad] = costFunction(theta, X, y)

%COSTFUNCTION Compute cost and gradient for logistic regression

% J = COSTFUNCTION(theta, X, y) computes the cost of using theta as the

% parameter for logistic regression and the gradient of the cost

% w.r.t. to the parameters.

% Initialize some useful values

m = length(y); % number of training examples

% You need to return the following variables correctly

J = 0;

grad = zeros(size(theta));

% ====================== YOUR CODE HERE ======================

% Instructions: Compute the cost of a particular choice of theta.

% You should set J to the cost.

% Compute the partial derivatives and set grad to the partial

% derivatives of the cost w.r.t. each parameter in theta

% Note: grad should have the same dimensions as theta

z = X * theta;

hx = 1 ./ (1 + exp(-z));

J = 1/m * sum([-y’ * log(hx) – (1 – y)’ * log(1 – hx)]);

for j = 1: length(theta)

grad(j) = 1/m * sum((hx – y)’ * X(:,j));

end

% =============================================================

end

（2）优化求极小值

% Set options for fminunc

options = optimset(‘GradObj’, ‘on’, ‘MaxIter’, 400);

% Run fminunc to obtain the optimal theta

% This function will return theta and the cost

[theta, cost] = …

fminunc(@(t)(costFunction(t, X, y)), initial_theta, options);

% [theta, cost] = …

% fminunc(@(t)(costFunction(t, X, y)), initial_theta);

% Print theta to screen

fprintf(‘Cost at theta found by fminunc: %fn’, cost);

fprintf(‘theta: n’);

fprintf(‘ %f n’, theta);

来自为知笔记(Wiz)

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Matlab&nbsp;fmincon函数用法

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Matlab fmincon函数用法