fmincon constraining some variables and not others

Hello,

I am trying to optimise a function depending on 6 optimisable variables using fmincon(). Some of the variables should be under inequality linear constrains, while others shouldn't have any constrain at all. Is there the possibility to enforce this with fmincon()?

I know that linear inequality constrains should be enforced by defining the system A · x ≤ b, but this forces me to impose a constrain over every element in x. Setting A(i,i) and b(i) as 0 seems a waste of CPU since fmincon() will probably keep using a constrain that actually is not.

One could think to define (A,b) and make their indices empty where no constrain should be, but of course this just concatenates A and b if they are vectors or is an error if A is a matrix.

Thank you for your answers.

Answer 1

[Matt J]

Setting A(i,i) and b(i) as 0 seems a waste of CPU since fmincon() will probably keep using a constrain that actually is not.

In theory, you can make A of type sparse, so that multiplications A(i,j)*x(j) for A(i,j)=0 will not be done explicitly. However, for such a small 6-variable problem, it doesn't make much sense. It is unlikely that these computations will consume noticeable additional CPU time.

[Ícar]

Thank you for the quick answer.

Answer 2

[Ameer Hamza]

"I know that linear inequality constrains should be enforced by defining the system A · x ≤ b, but this forces me to impose a constrain over every element in x. Setting A(i,i) and b(i) as 0 seems a waste of CPU since fmincon() will probably keep using a constrain that actually is not."

Why do you think so?

Conside the constraint

You will define it like this

A = [1 0 0 0 1 0];
B = 2;

This does not impose any constraint on x2, x3, x4, and x6.

[Ícar]

Thank you for the quick answer. Mmm what I meant was more of the style of having some constrains over some variables say, x1<3, x5<68, but not over the others.

If I am imposing a 0 · v ≤ 0, I suspect that fmincon() will treat it as any other constrain over the variable v, only to "find out" that this constrain will not effectively impose anything. Another person mentioned that the matrix A can be declared sparse (and thus the multiplications in the system A * x ≤ b that are of the style 0 · v ≤ 0 wouldn't be performed). Also probably this is not a huge CPU burden for my number of variables.

[Matt J]

Simple bounds like x1<=3, x5<=68 should not be expressed using the A,b matrices. You should use the lb, ub arguments for those. In any case, recent versions of Matlab will pre-analyze your A,b matrices to see if they contain any simple bounds and rewrite your constraints automatically.

[Ícar]

I was aware of that for the simple bounds, I tried to just use the simplest example I could imagine of to get my point across. :) But should have picked an unequivocal one. Thank you!