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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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The first reference which formulated k-means problem as MIQCP using big-M constraint

From your question, I can't tell if you're asking about the origin of big-M constraints or the origin of k-means via MIP. I'm going to assume that you mean the latter, and it's a deep hole. The paper ...
Brannon's user avatar
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Enforcing Order in a Linear Programming Question

For simplicity, I will omit the $t$ index. You want to enforce $$x_1+x_2+x_3\ge d \implies x_4=0.$$ Equivalently, enforce the contrapositive $$x_4>0 \implies x_1+x_2+x_3< d.$$ Let $\epsilon$ be ...
RobPratt's user avatar
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