how to impelement u1<=u2<=u3 as linear inequality

in my optimizations i have following constraint u1<=u2<=u3 i think i have to use linear equality constaints. ie.Ax<b I am using x = fmincon(fun,x0,A,b,Aeq,beq,lb,ub,nonlcon). Any one has any idea? thanks in advance for the help

Answer 1

[Matt J]

A=[1 -1 0; 0 1 -1]; b=[0;0];

[Raihan Ul Islam]

you mean that u1-u2<=0 and u2-u3<=0 what about u3 <u1?

[Matt J]

What about it? It's not one of the constraints you posted, but you would implement it as u3-u1<=0 similar to the others.

[John D'Errico]

@Raihan - You stated that you wanted to implement the combined constraint:

u1<=u2<=u3

That is short hand for two inequalities:

u1 <= u2

AND

u2 <= u3

However, transitivity applies here. If u1<=u2, AND u2<=u3, then you need never bother to apply a third constraint, that is, it is always true that u1<=u3.

You wrote u3<u1 in your comment, and of course this MUST be always false, since I just said that the two constraints imply that u1<=u3.

[Raihan Ul Islam]

Thanks for the information.