Acta Mathematica Vietnamica

Acta Mathematica Vietnamica

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LEXICOGRAPHICAL CHARACTERIZATION OF THE FACES OF CONVEX SETS

J. E. MARTINEZ-LEGAZ

pp. 207-211

Abstract

We prove that a nonempty proper subset of a convex set $C$ is a face if and only if it is the set of points where a linear mapping achieves its lexicographical maximum over $C$.