prioritizing a constraint

[Jack1]

I have two constraints on `x`

L<=x<=U

A<=x<=B

and I would like the optimizer to satisfy the first over the other; however, I would still like to keep the second one since I can adjust the bounds. 

I am currently getting an infeasible soln with both of them. But, if i added a slack term to the first then the soln is feasible, but, that constraint becomes easily violated which I don't want. So, I added a slack to the second constraint, but, then run into infeasibilities.

Can you pls advise of alternatives? Maybe I can appropriately bound the slack term that's in the second constraint? Thank you.

[Johan Löfberg]

the only way to do that if slacks don't work as you want is to model some logic using binary variables (or simply solving a sequence of problems)

[Jack1]

Thank you. And one more Q: since there are two constraints in the above on `x` --> does this imply that the optimizer would always respect both? Or, can it choose to go with either the lower or upper bound on a run? 

For instance, if U is tighter than B (i.e., U <= B), then, could it not be the case that the optimizer can choose to go with the relaxed one B or would it have to satisfy U as well? I don't think so because there is no rule in the optimizer saying to prioritize the first constraint over the second? But, am not sure. 

[Johan Löfberg]

if you have x<=1 and x<=2, the second constraint is redundant and will be eliminated before the solver even starts

A solver satisfies all constraints in a model, if you want otherwise you will have to model a more complex model involving OR constraints modelled using binary variables etc

[Johan Löfberg]

i.e., the model you write in your first post is simply max(L,A) <= x <= min(U,B)