Set gradual parameter constraints in fmincon

Hello everyone,

Here is my problem, I want to optimize a function with several parameters. Let's say that my function is: modelFun=@(a) a(1)x^2 +a(2);, so my paramers are a(1) and a(2). Therefore, I want fmincon to give me those parameters given a noise measure. Additionally, i know the bounds of the parameters lb=[0 0]; ub=[4 2]; So far, this is easy to implement: fminxon(modelFun,seed,[],[],[],[],lb,up);. However i know one more constrain for the parameters and it's that a(1)>a(2). This is the constraint I can not implement, and i'm asking for your help to implement it if possible.

I think it can not be implemented neither with inequality constraints nor nonlinear constraints.

Do you have any idea? Thank you very much, Oscar

Answer 1

[John D'Errico]

Why cannot it be implemented? This is not even a nonlinear inequality constraint. Use the linear inequality constraints.

Is your fear that they implement the constraint with an >= instead of > ?

So then just require that

a(1) >= a(2) + delta

for some REASONABLY small value of delta. I would suggest using a larger value of delta than you have for TolCon, so that any constraint violation will not be a problem.

[Óscar]

Thanks John, right after you wrote this comment i realize that i can use A and b in the simples way A=[-1 1]; b=[0]; and that is equivalent to a(1)<a(2). So i dont need that delta.