Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

Gerd Wachsmuth

Brandenburgische Technische Universität Cottbus-Senftenberg, Institute of Mathematics, 03046 Cottbus, Germany

wachsmuth@b-tu.de

Keywords

  • Polyhedricity
  • polyhedric set
  • directional differentiability
  • projection
  • vector lattice
  • strong stationarity
  • second-order conditions

Mathematics Subject Classification

49K21, 46A55, 46N10

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Suggested citation

G. Wachsmuth. “A Guided Tour of Polyhedric Sets: Basic Properties, New Results on Intersections and Applications.” Journal of Convex Analysis 26 (2019), No. 1, 153–188. https://doi.org/10.68381/jca26010

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Published by Heldermann Verlag, 2019. Rights now held by Banach Press LLC.