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A branch of geometry dealing with convex sets and functions. Polytopes, convex bodies, discrete geometry, linear programming, antimatroids, ...
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Complexity of finding one vertex of a nonempty polytope
Let $P$ be a polytope given by some half-space description: $P=\{x\in\mathbb{R}^n: Ax\leq b\}$ for some $A\in\mathbb{R}^{m\times n}, b\in\mathbb{R}^m$, $m\geq n$. Assume that $x_0\in P$ for some given …