Genericity Results in Linear Conic Programming: A Tour d’Horizon

Mirjam Dür, Bolor Jargalsaikhan, Georg J. Still

Research output: Contribution to journalArticleAcademicpeer-review

7 Citations (Scopus)

Abstract

This paper is concerned with so-called generic properties of general linear conic programs. Many results have been obtained on this subject during the last two decades. For example, it is known that uniqueness, strict complementarity, and nondegeneracy of optimal solutions hold for almost all problem instances. Strong duality holds generically in a stronger sense, i.e., it holds for a generic subset of problem instances.
In this paper, we survey known results and present new ones. In particular we give an easy proof of the fact that Slater’s condition holds generically in linear conic programming. We further discuss the problem of stability of uniqueness, nondegeneracy, and strict complementarity. We also comment on the fact that in general, a conic program cannot be treated as a smooth problem and that techniques from nonsmooth geometric measure theory are needed.
Original languageEnglish
Pages (from-to)77
Number of pages94
JournalMathematics of operations research
Volume42
Issue number1
DOIs
Publication statusPublished - 1 Feb 2017

Keywords

  • conic optimization
  • generic properties
  • Slater’s condition
  • uniqueness and nondegeneracy of optimal solutions
  • strict complementarity
  • stability

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