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I am given a set of inequalities $v_1\ge v_2\ge \cdots\ge v_n\ge 0$, $q_2\le \sum_{i=1}^n p_iv_i\le q_1$, with $\{p_i\}_{i=1}^n,\ q_1,q_2$ positive reals, and only one bound for the coordinates: $v_1\...

Given an $n$-dimensional vector $\mathbf{c}\in [0,1]^n$, let $\Delta_{\mathbf{c}}$ be the set of points $\{\mathbf{x}\in [0,1]^n: \langle \mathbf{c},\mathbf{x} \rangle \le 1\}$, where $\langle \mathbf{...

Suppose you have two polytopes $P_1, P_2 \in \Bbb{R}^n$ given by $$ P_1 = \lbrace x: A_1 x \le b_1\rbrace$$ $$ P_2 = \lbrace x: A_2 x \le b_2\rbrace $$ I wish to find their convex hull, that is a ...