Weakly Motzkin decomposable evenly convex sets

M. Rodríguez Álvarez, J. Vicente Pérez, J. E. Martínez Legaz

In recent years, different families of convex sets which can be decomposed as the (Minkowski) sum of a bounded convex set and a convex cone have been introduced. In particular, M-decomposable sets are the sum of a compact convex set and a closed convex cone (the corresponding recession cone), being polyhedral convex sets a subclass of this family of closed convex sets. More recently, the class of e-polyhedra (the solution sets of finite linear systems containing strict inequalities) was studied and it was proved that any e-polyhedron can be expressed as the sum of an e-polytope (bounded e-polyhedron) and its recession cone. In this talk, we extend this kind of decomposition to the broader class of evenly convex sets, that is, the intersections of families of open half-spaces (Fenchel 1952).

Keywords: Convex sets, linear inequality systems

Continuous Optimization II
June 10, 2025  3:30 PM
MR 3

J. Vicente Pérez

J. Castro Pérez, L. F. Escudero Bueno, J. F. Monge Ivars

J. Rückmann

X. Moreno-Vassart, F. J. Toledo, V. Herranz, V. Galiano