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A structural geometrical analysis of weakly infeasible SDPs

Bruno F. Lourenço (flourenco.b.aa***at***m.titech.ac.jp)
Masakazu Muramatsu (muramatu***at***cs.uec.ac.jp)
Takashi Tsuchiya (tsuchiya***at***grips.ac.jp)

Abstract: In this article, we present a geometric theoretical analysis of semidefinite feasibility problems (SDFPs). We introduce the concept of hyper feasible partitions and sub-hyper feasible directions, and show how they can be used to decompose SDFPs into smaller ones, in a way that preserves most feasibility properties of the original problem. With this technique, we develop a detailed analysis of weakly infeasible SDFPs to understand clearly and systematically how weak infeasibility arises in semidefinite programming.

Keywords: Weakly infeasible problems, semidefinite feasibility problem

Category 1: Linear, Cone and Semidefinite Programming

Category 2: Linear, Cone and Semidefinite Programming (Semi-definite Programming )

Citation:

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Entry Submitted: 11/23/2013
Entry Accepted: 11/27/2013
Entry Last Modified: 05/25/2014

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