fminsearch with side conditions

Hey,

I have a equation where I am looking for the minimum. The equation has 6 variables, but due to interdependencies it can be reduced to 4.

My problem is that there is a side condition which I cannot translate into the function and therefore the results are wrong.

The side condition is that 3 of those variables have to sum up to 1, which I have realized as :

c=1-a-b

and that the sum of a and b ahs to be less or equal to 1.

So it is possible that c is zero, but not less.

And that last side condition wont o into my function. I can surely replace c by 1-a-b, but how do I get the a+b<=1 into my function

Many Thanks in advance and best regards

Answer 1

[John D'Errico]

Generally, the solution is to not use fminsearch. Use a better optimizer instead. It will be faster, and you will get a better answer. What can I say?

FMINCON would be my first recommendation. However, other tools, like LSQLIN or INTLINPROG might be appropriate, since I don't know your actual problem.

CAN you use fminsearch? Well, yes. You could do so. If I were pressed, I would start by replacing c completely in your problem, replacing it with 1-a-b. Then I would use a penalty function approach. Start out with an initial value for fminsearch that satisfies your requirements, that a+b <= 1. INSIDE your objective function, IF fminsearch passes in a set of parameters where a+b is NOT acceptable, then don't even bother trying to evaluate the function, just return inf. Fminsearch will not be fazed by this infinite penalty on the objective, and it should produce a result that satisfies your goals as long as you start with a feasible point.

If you want a better, more complete answer, then I would need to see more information. What is your ACTUAL problem? Perhaps this is a simple linear problem in some way, and a tool such as intlinprog or lsqlin would be sufficient.

[Marc Laub]

I was not aware of FMINCON. I just used fminsearch, to be exact fminsearchbnd because some global minimums that are not in a certain interval dont have a physical meaning.

[John D'Errico]

If you have the optimization toolbox, use fmincon as a better choice here. If you don't have that TB then get it, as it is a terribly useful toolbox IMHO. If you cannot get that toolbox, then use fminsearch as I described (or fminsearchbnd, written by some hack who I can't remember his name.)

[Marc Laub]

I have it.

I tried it with fmincon but while trying I figured out mutiple non linear side conditions that also should not be violated. Guess Ill try to solve this with a penalty approach within fmincon, just have to figure out where fmicon evaluates those values.