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Explicit equation for border of the Minkowski sum of sets

Assume we have sets of the form $$ M_j = \{x\in\mathbb{R}^d : f_j(x) \le 0,x \ge 0\} $$ where $x\ge 0$ means $x_i \ge 0 \quad \forall i=1,\dots, d$. Goal I am looking for an (explicit) representation ...
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