Ascent and descent cones of ordered median block functions

J. Grzybowski, J. Kalcsics, S. Nickel, D. Pallaschke*, R. Urbański

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we study properties of a special class of ordered median functions, called block-functions. These are ordered median functions which belong to a generating binary (row)-vector of the form λ = (0, 0, . . , 0, 1, 1, . . , 1, 0, 0, . . , 0) ∈ Rn, called a block vector. The aim of this paper is to explicitly determine the simplicial complexes and all steepest descent and ascent directions of descent and ascent cones of ordered median block-function.

Original languageEnglish
Pages (from-to)507-522
Number of pages16
JournalOptimization
Volume67
Issue number5
DOIs
Publication statusPublished - 25 Jan 2018

Keywords

  • ascent- and descent directions
  • convex analysis
  • Ordered median functions

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