How can I solve a min problem for integral?

Hello.

I've been looking through optimization problem examples and I am not sure how I should solve my problem. The problem is to find a minimum of definite integral such as int(f1(x)-f2(A,B,C,x)). I.e. I want to find A, B and C which will give me minimum value of that integral.

Any advice would be nice.

Answer 1

[Alan Weiss]

Let's reformulate your problem as numerical, not symbolic, because you are going to want a numeric answer.

Also, let's call your three parameters [A,B,C] = y.

So you have a function of y that you want to minimize. Is this a constrained or unconstrained problem? I mean, are there limits on the values in y?

Suppose not. Then for any value of y, I suppose you have a function defined on your MATLAB path that accepts a vector of points x and returns a vector of integrand values:

 myintegrand(x,y) = f1(x) - f2(x,y);

Your objective function is

 r = @(y)integral(@(x)myintegrand(x,y),xmin,xmax);

Then solve the problem starting from an initial guess y0 to the unknown parameters:

 ysolution = fminunc(r,y0)

Alan Weiss

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