For maximizing the objective function $\sum_i{d_i y_i}+ A x - B \cdot \mathbb{I}_{x>0}$, how can I linearize $ A x - B \cdot \mathbb{I}_{x>0}$ term where $d_i, A$ and $B$ are positive constants and $x, y_i$ are continuous non-negative variables? Can you explain the logic of linearization? There are many other constraints involving $y_i, x$.
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$\begingroup$ Minimize or maximize? $\endgroup$– RobPrattCommented Sep 8, 2020 at 22:43
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$\begingroup$ @RobPratt Maximize $\endgroup$– Al GuyCommented Sep 8, 2020 at 22:53
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1 Answer
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If $M$ is a (small) upper bound on $x$, introduce a binary variable $z$ and big-M constraint $x \le M z$. The idea is that $x>0$ implies $z=1$. Now use $B z$ in the objective.
