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Journal of Convex Analysis 26 (2019), No. 1, 153--188
Copyright Heldermann Verlag 2019

A Guided Tour of Polyhedric Sets: Basic Properties, New Results on Intersections and Applications

Gerd Wachsmuth
Brandenburgische Technische Universitšt Cottbus-Senftenberg, Institute of Mathematics, 03046 Cottbus, Germany

The aim of this contribution is twofold. On the one hand, we give some new results concerning polyhedric sets. In particular, we show that sets with pointwise lower and upper bound are polyhedric in many important function spaces. Moreover, we show that the intersection of such a set with finitely many hyperplanes and half-spaces is polyhedric. We also provide counterexamples demonstrating that the intersection of polyhedric sets may fail to be polyhedric. On the other hand, we gather all important results from the literature concerning polyhedric sets in order to give a complete picture of the current knowledge. In particular, we illustrate the applications of polyhedricity.

Keywords: Polyhedricity, polyhedric set, directional differentiability, projection, vector lattice, strong stationarity, second-order conditions.

MSC: 49K21, 46A55, 46N10

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