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Removing min operator from max objective

A simple intuition would be that the second inequality is stronger ($\geq$) than the first one. Therefore, dropping the minimum would allow more flexibility, but I do not think they are equivalent.
Abdellah's user avatar
1 vote

How to reformulate the BigM constraints into its equivalent Convex-hull formulation?

Rewrite as \begin{align} &\text{minimize} & s_1 + s_2 \\ &\text{subject to} & (s_2 - s_1 \le -\alpha) &\lor (s_1 - s_2 \le -\beta) \\ && \text{LB} \le s_i &\le \text{...
RobPratt's user avatar
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2 votes

On Linear Relaxation of Standard Quadratic Programming

The LP you have shown has optimal objective value equal to the minimum element of $Q$, for any symmetric $Q$, regardless of its definiteness. This can be seen as follows: Sum over all elements of $X$ ...
Mark L. Stone's user avatar
2 votes

How to avoid division by zero with a binary variable at the denominator in a network assignment problem?

The fundamental question to address is the time consumption to associate with a user that is not served ($a_{mn}=0$ for all $n,$ implying $\phi_{mn} = 0$ for all $n.$ Possibilities include no time ...
prubin's user avatar
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5 votes

How to model an optimization problem with mutual exclusivity of two variables, without introducing integer variables?

You want to enforce $L_t=0 \lor S_t=0$, where both variables are nonnegative. Here are three ways: The approach in your question, but with $z_t$ binary. Nonlinear “complementarity” constraint $L_t ...
RobPratt's user avatar
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