First-order methods for the convex-hull membership problem and applications

Rafaela Filippozzi, Douglas S. Gonçalves, Luiz Rafael Santos


Let A := {v1 , v2 , . . . , vn } be a finite subset of Rm and consider a given point  p ∈ Rm . The convex hull membership problem (CHMP) consists in deciding whether p ∈ conv(A), where conv(A) denotes the convex hull of A. This problem is related to fundamental concepts in linear programming and nds important applications in computational geometry [3, 4]. [...]

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