How can ı solve this constraint optimization problem?

Answer 1

[Bruno Luong]

Hint: you should find

x=y=1

Answer 2

[Star Strider]

I get the feeling that this is likely homework.

It would likely be easiest to use the fmincon function, although there are several functions that could do what you want. Note that the optimisation functions minimise the function they are given, so to maximise it, calculate the negative of the function you supply to fmincon.

[Sinem Senel]

Actually ı tried fmin func but matlab always gave me an error ıdk what ı am doing wrong. And ı look some other examples they all have more constraints, x0 etc. I tried to solve this only using upper and lower bound But it could not work.

Answer 3

[John D'Errico]

Many things you can do, but since this is your homework, and there are already answrs posted, I'll just suggest a couple of things. Why not plot it? Look at the surface. Look at contours of the function on that domain.

Other things. You could differentiate it. Is there a zero of the gradient vector in that region? Is that at a maximum or minimum?

You could use optimization tools. FMINCON comes to mind. Or GA, or any of a number of tools.

[Sinem Senel]

Actually it is not my homework, ı just wabt to learn how can ı solve optimization problem in matlab. And I want some optimization problem from my Teacher to apply in matlab.But ı could not solve. I look to many page for that and could not find similar one. All of them have more Constraint.

[Bruno Luong]

Yes because they are designed to handle all kinds of constraints. You don't need those constraints that your problem doesn' have, you don't have to set them. Usually that just meant to put an empty bracket '[]' in the corresponding input argument.

And I can find an example similar to your problem, right in the doc page of fmincon, after expanding the section "Minimize with Bound Constraints".

[Sinem Senel]

I will look thank you so much. And also ı have one question too. I am sorry for my basic Question I am new at thıs things. Matlab want to describe x0, how can ı describe with this limited information. I try to use x0=[] but ıt gave me an error

[Bruno Luong]

x0 must be provided base on what a priori your knowledge of where the soluion would be (yeah you definitvely need to read about optimization tools). In this example I direct to you, they select simply as

0.5*(lb+ub)

which is the middle point of the box, heuristically chosen.

[Sinem Senel]

Thank you so much.you have no idea how much you helped me. Yeah I sould find a good article about optimisaon in matlab.