Constraint concerning the maximum of a set of variables

[Xu Wang84]

Hi, 

I was wondering if I am able to write a constraint with description of the maximum of a set of variables. 

E.g. :

Y <= max(X)

where X is an array of variables. 

Thanks a lot.

Xu

[Johan Löfberg]

Yes, but it is a nonconvex constraint and will lead to a mixed-integer problem

[Xu Wang84]

Does it solve though?

[Johan Löfberg]

You never know. It is an integer program so it can be anything from trivial to unsolvable

The following MILP is not solved by any MILP solver. 

intvar x1 x2 x3 x4

sdpvar r1 r2 r3

obj = 2*x1+2*x2+2*x3-3*x4;

C = [2*x1+x2+x3-2*x4-2*r1 == .1;

     x1+2*x2+x3-2*x4-2*r2 == .1;

     x1+x2+2*x3-2*x4-2*r3 == .1;

     2*x1+2*x2+2*x3 >= .1

     0 <= [r1 r2 r3] <= .9];

 

 solvesdp(C,obj)

Make sure your variables are bounded so your big-M formulation of the nonconvex max operator works

http://users.isy.liu.se/johanl/yalmip/pmwiki.php?n=Tutorials.Big-MAndConvexHulls