Run fmincon multiple time

Hi

I am trying to maximize an function(x,y) over (x,y)

x^2+y^2+b, subject to 0<x<1 and 0<y<1. and b is between 0 and 20.

Now, I want to run fmincon on this function 20 times (for b=0, b=1, b=2..... and so on). I also want to save the optimal (x,y) with the coresponding b so that I can plot this function later.

I have looked up ( http://www.mathworks.com/help/optim/ug/nonlinear-equality-and-inequality-constraints.html ), How should I modify the code so that it will do the above?

[Matt J]

Your problem is a quadratic program. It is therefore better to use quadprog as opposed to fmincon.

Aside from that, there is no point in repeating the optimization for multiple b, as you describe. The value of b doesn't affect the maximizing coordinates (x,y), which will always be x=y=1.

[Aniruddha Phatak]

You are trying to maximize the function (which anyway has a straightforward answer x=y=1), but the function fmincon finds the (x,y) values that minimizes the function . Also, the value of b makes no difference to the maximized or minimized value. Perhaps you meant x^2-y^2 with perhaps b as a multiplying factor rather than just an additive factor? (Or perhaps I didn't read your question right in the first place?)

[JJ]

yes, but I will apply this process to a more complicate function, subject to more complicate constraint, what I am looking for is the process that will solve this problem.

[Matt J]

But because your example isn't similar enough to your true problem, you are unlikely to get a response that is meaningful to your true problem.

[JJ]

Please refer to this question.

http://www.mathworks.com/matlabcentral/answers/152196-help-run-fmincon-repeatedly

Answer 1

[Matt J]

Your example is a straightforward application of QUADPROG

 [xy, fval]=quadprog(-eye(2),[0;0],[],[],[],[],[0;0],[1;1])

b=0:20;

fval=fval+b;

[JJ]

http://www.mathworks.com/matlabcentral/answers/152196-help-run-fmincon-repeatedly, please refer to this page

[Matt J]

I have the vague impression that this is what you're looking for

http://www.mathworks.com/help/optim/ug/passing-extra-parameters.html

It will tell you how to pass 'b' to the objective function as fixed data.