In fmincon function, how can I impose non-strict constraints?

In fmincon, I know MATLAB can set constraints like a+b<=1 and a<=1, but what about a+b<1 and a<1?

Answer 1

[Alan Weiss]

There is a tolerance called TolCon that gives the wiggle room for constraint violation. So, if you have options such as

 options = optimoptions('fmincon');

then, similar to Walter's suggestion, you can try to enforce

 a + b <= 1 - options.TolCon; % in a linear inequality constraint
 a <= 1 - options.TolCon; % in a bound

Alan Weiss

MATLAB mathematical toolbox documentation

Answer 2

[Torsten]

Strict constraints (like a<1 or a+b<1) don't make sense in optimization.

Usually, you can only guarantee solutions over compact (i.e. closed and bounded) feasible regions.

Conditions like a<1 or a+b<1 lead to open (i.e. non-closed) regions.

Best wishes

Torsten.

Answer 3

[Walter Roberson]

a+b <= 1-eps
a <= 1-eps