# Tag Info

### Why are integer minimax problems hard?

This is going to be a hand-waving argument: perhaps this has been formalized in the literature someplace. I think the issue is that the linear relaxation is in some sense more compatible with the p-...
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### Why are integer minimax problems hard?

I can see two reasons why branch-and-bound based solvers can have a hard time solving these problems: the linear relaxation may be bad (as stated above); these models have typically (exponentially) ...

### Why are integer minimax problems hard?

I will give you a little more insight based on my latest experience solving minimax (or maximin) integer programs. Sorry I will be a bit self-citing here. Indeed, the main reason that can explain the ...
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### How can I express this max-min in CPLEX?

You can model this as a maxmin problem by introducing an auxiliary variable $\theta$: \begin{align} \max&\quad\theta &\\ \text{s.t.}&\quad\theta \leq \sum_{c=1}^C x_{uc}d_{uc} & \...
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### How can I express this max-min in CPLEX?

Maximize an auxiliary variable $z$ subject to the constraints $z\le \sum_{c=1}^C d_{u,c}x_{u,c}\ \forall u$.
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### How to determine least time required to complete all tasks?

Minimizing the sum of all assignments: this is the classical version of the assignment problem. The Hungarian algorithm solves it in polynomial time. Minimizing the maximum of all assignments: this ...
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### Convex-Constrained Nonconvex-Nonconcave Minimax Problem

I got bad news for you: The problem is as long as you care about the inner max being the actual max and not just some local maxima (which might make sense with multiple roll outs for a game theory ...
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### how to implement a constraint with max/min function in pyomo

Maybe you can replace your equality constraint with two inequality $\leq$ and $\ge$ constraints. Also, have a look at this link
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