How to express z<=x/y?

Nonconvex
Apr 23, 2022
A
#1

In my constraint, z<=x/y. x,y,z are variables. How do I express this expression in the syntax accepted by CVX?

J
#2

this is neither convex nor concave, so it can’t be done in cvx. see

1 reply
A
#3
Replying to #2

I know what you mean. In the code, I’ll write it as
[x z;y 1]==semidefinite(2);
But now my program is infeasible, and I’m looking for constraints one by one, so considering whether this constraint is the problem, I wonder if there are other solutions to express this formula.

1 reply
J
#4
Replying to #3

This will force [x z;y 1] to be symmetric, if I didn’t get it wrong from The Basics — CVX Users' Guide. So you will have z=y, which might not be what you wanted.

M
#5

I am surprised that [x z;y 1]==semidefinite(2); did not produce a warning message about being non-symmetric. i don’t know what it does, but I doubt it’s anything good. It is not a magic formulation for convex alchemy to convert a non-convex constraint into a convex constraint.