Identifying redundant linear constraints in systems of linear matrix inequality constraints

Shafiu Jibrin, Daniel Stover

Research output: Contribution to journalArticlepeer-review


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
Issue number5
StatePublished - 2007


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

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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