Optimization with infinite constraints

Hello,

I must face the following contraint in my optimization (simplified):

a-b(x,a) < 0                                  a >= 0
% X: parameter vector to be optimized
% a: additional variable of length 1

I have come across 'fseminf' function, which seems to be exactly what I was looking to. However, it only takes into account close intervals for 'a'. I would need this constraint to be met for any positive real value of a with a precision of thousandths.

Does anything like this exist? Could any of you give me a hand?

Answer 1

[Nicolas Schmit]

1) Augment your parameter vector X with a.

Xaug = [X; a];

2) Define a-b(x,a) < 0 as a nonlinear constraint.

3) Define the bounds of a.

lba = 0;
uba = inf;

4) Solve the problem using fmincon (or another optimization routine).