fminsearch with side conditions
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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 :
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
John D'Errico on 17 May 2022
Edited: John D'Errico on 17 May 2022
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.