如果变量取决于优化变量，如何编写程序进行优化? [英] How to code a program for optimization if a variable depends on optimization variables?

问题描述

在进行优化时，我在Matlab中有一个问题.假设我想对向量x

I have a question in matlab when doing optimization. Suppose I want to to do an optimization problem on a vector of x

min_x f(x,c)这样的sum(x)=1.对于每个固定的x，c是一个常量，例如

min_x f(x,c) such that sum(x)=1. For each fixed x, c is a constant, say for example

(x.*a+c).^(1./alpha)+(x.*b+c).^(1./alpha)=1

其中a,b,alpha是已知的.

该算法适用于每个固定的x，因此sum(x)=1，我们需要从

The algorithm is for each fixed x such that sum(x)=1, we need to find c from

(x.*a+c).^(1./alpha)+(x.*b+c).^(1./alpha)=1 

并计算f(x,c)，然后我们更新一个新的x.

and compute f(x,c), then we update a new x.

是否可以在matlab中使用fmincon解决问题?我想放

Is it possible to use fmincon in matlab to solve the problem? I want to put

(x.*a+c).^(1./alpha)+(x.*b+c).^(1./alpha)=1 

用于 fmincon 中的非线性约束，但我想知道它是否有效，因为我们不知道如何根据x明确编写c.

for the non linear constraint in fmincon, but i wonder if it is valid as we do not know how to write c explicitly in terms of x.

推荐答案

• 使用solve根据x
显式地编写c
• 将f(x,c)定义为仅x的函数
• c被其表达式替换
• 开始优化
• Use solve to write c explicitly in terms of x
• Define f(x,c) to be a function of x only
• c is replaced by its expression
• Start the optimization

请仔细阅读评论

% Given a, b, alpha
a = 2; b = 5; alpha = 1;

% Unknown x, c
syms x c

% Relation between x and c
eq = (x.*a+c).^(1./alpha)+(x.*b+c).^(1./alpha)== 1 ;

% Mention only c, x will be considered as independent variable
% The solution gives c in terms of x
c = solve(eq, c);

% Transfom syms variable into function handle variable 
c = matlabFunction(c);
% c(x) = x.*(-7.0./2.0)+1.0./2.0


% Define f as a function of x only, c is a constant having x as parameter
 fun =@(x)f(x, c(x));

% optimization starts here 

 [x, fval] = fmincon(fun,x0,A,b,Aeq,beq,lb,ub,nonlcon,options);


% Given function in terms of x and c
function y = f(x,c)
    y = 2.*x + c;
end

这篇关于如果变量取决于优化变量，如何编写程序进行优化?的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持IT屋！