I'm struggling with one equation within a subtour elimination constraint.

$$\sum_{i \in S} \sum_{j \in S, j<i} y^t_{ij} \le \sum_{i \in S} z_{it} -z_{kt} \quad S \subseteq M \quad t \in T \quad \text{for some} \ k \in S$$


$$y^t_{ij} = z_{it} = \{0,1\} \quad \text{(binary decision variable)}$$

I'm not familiar with the term $\textrm{argmax}$. What's the exact meaning in this equation? What I've read is that an argument $z_{jt}$ must be found to maximize the function $f$. But there is no function, isn't it?

The whole equation is part of a MIP callback to add a lazy constraint (implemented with Gurobi solver).


I could be wrong, but I believe it can be read here simply as "the $j$ such that $z_{jt}$ is at its maximum value".

  • 2
    $\begingroup$ I agree with this. $\endgroup$ – Mankind May 19 '15 at 21:06

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