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The Slater condition is generic in linear conic programming

Mirjam Duer(duer***at***uni-trier.de)
Bolor Jargalsaikhan(B.Jargalsaikhan***at***rug.nl)
Georg Still(g.still***at***math.utwente.nl)

Abstract: We call a property generic if it holds for almost all problem instances. For linear conic problems, it has been shown in the literature that properties like uniqueness, strict complementarity or nondegeneracy of the optimal solution are generic under the assumption that Slater's condition is fulfilled. The possibility that Slater's condition generically fails has not been excluded. In this paper, we close this gap by proving that Slater's condition is generic in linear conic programs. We also summarize genericity results of other properties and discuss connections among them.

Keywords: Conic programs; Slater's condition; generic properties

Category 1: Linear, Cone and Semidefinite Programming

Category 2: Infinite Dimensional Optimization (Semi-infinite Programming )

Citation: Preprint, 2012.

Download: [PDF]

Entry Submitted: 11/09/2012
Entry Accepted: 11/09/2012
Entry Last Modified: 11/09/2012

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