Multi-function optimization

4 次查看（过去 30 天）

显示更早的评论

Idossou Marius Adom 2019-12-3

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/494631-multi-function-optimization

评论： Idossou Marius Adom 2019-12-4

采纳的回答： Matt J

在 MATLAB Online 中打开

Hi.

I have a function f(x,a) where a is a parameter that is exogenously provided. I want to minimize f(x,a) for different values of a (a1 a2 a3 ...) independently. Is there any way to do that without using a for loop ?

If I consider defining f(x,[a1 a2 a3 ...]) as a multidimensional:

function f = obj(x,a)
    f(1) = f(x,a1);
    f(2) = f(x,a2);
    f(3) = f(x,a3);
    .
    .
    .
end

and then minimize f by providing the vector a=[a1 a2 a3 ...], Matlab will not consider the components of the function as independent as I want. Do you have any solution ?

Thank you.

1 个评论
显示 -1更早的评论隐藏 -1更早的评论

Walter Roberson 2019-12-3

You can hide the loop with arrayfun but otherwise you should still be using a loop of some kind as the objectives are independent.

请先登录，再进行评论。

请先登录，再回答此问题。

采纳的回答

Matt J 2019-12-3

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/494631-multi-function-optimization#answer_404554

编辑：Matt J 2019-12-3

在 MATLAB Online 中打开

You would need something like the following,

options=optimoptions(@fminunc,'SpecifyObjectiveGradient', true);
allX = fminunc(@(x)obj(x,a),x0,options);
function [ftotal,gradient] = obj(x,a)
    delta=1e-6;
    f0=getfs(x,a);
    ftotal=sum(f0);
    
    if nargout>1
        gradient=(getfs(x+delta,a)-f0)./delta; %finite difference approx
    end
end
function f=getfs(x,a)
    f(1) = f(x(1),a(1));
    f(2) = f(x(2),a(2));
    f(3) = f(x(3),a(3));
    .
    .
    .
end

You could also of course implement an analytic version of the gradient calculation, instead of using finite differences.

However, you should keep in mind that a for-loop may be advantageous if the a(i) are separated by small increments. That usually means that the optimal solution x(i) is a good initial guess of x(i+1), so you don't have to do as many iterations in the next pass of the for-loop..

7 个评论
显示 5更早的评论隐藏 5更早的评论

Matt J 2019-12-4

But, then, is it sure the fminunc is minimizing the components of f independently ?

As you can see, the objective function we have defined in the above scheme is additively separable: it is the sum of independent terms f(x(i),a(i)) and therefore the minimization of the sum is equivalent to minimizing each f((xi),a(i)) independently.

Idossou Marius Adom 2019-12-4