Genericity Results in Linear Conic Programming-A Tour d'Horizon

• 成果类型: Article
• 署名作者: Duer, Mirjam; Jargalsaikhan, Bolor; Still, Georg
• 署名单位: Universitat Trier; University of Groningen; University of Twente
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2016.0793
• 发表日期: 2017
• 页码: 77-94
• 关键词: duality

摘要

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.