Identifying redundant linear constraints in systems of linear matrix inequality constraints

Shafiu Jibrin, Daniel Stover

Research output: Contribution to journalArticle

Abstract

Semidefinite programming has been an interesting and active area of research for several years. In semidefinite programming one optimizes a convex (often linear) objective function subject to a system of linear matrix inequality constraints. Despite its numerous applications, algorithms for solving semidefinite programming problems are restricted to problems of moderate size because the computation time grows faster than linear as the size increases. There are also storage requirements. So, it is of interest to consider how to identify redundant constraints from a semidefinite programming problem. However, it is known that the problem of determining whether or not a linear matrix inequality constraint is redundant or not is NP complete, in general. In this paper, we develop deterministic methods for identifying all redundant linear constraints in semidefinite programming. We use a characterization of the normal cone at a boundary point and semidefinite programming duality. Our methods extend certain redundancy techniques from linear programming to semidefinite programming.

Original languageEnglish (US)
Pages (from-to)601-617
Number of pages17
JournalJournal of Interdisciplinary Mathematics
Volume10
Issue number5
DOIs
StatePublished - 2007

Fingerprint

Semidefinite Programming
Linear Constraints
Inequality Constraints
Linear matrix inequalities
Matrix Inequality
Linear Inequalities
Linear programming
Redundancy
Cones
Normal Cone
Linear Function
Duality
NP-complete problem
Objective function
Optimise
Requirements

Keywords

  • Linear matrix inequalities
  • Normal cone
  • Redundancy
  • Semidefinite programming

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Identifying redundant linear constraints in systems of linear matrix inequality constraints. / Jibrin, Shafiu; Stover, Daniel.

In: Journal of Interdisciplinary Mathematics, Vol. 10, No. 5, 2007, p. 601-617.

Research output: Contribution to journalArticle

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