Semidefinite diagonal directions Monte Carlo algorithms for detecting necessary linear matrix inequality constraints

Shafiu Jibrin, Arnon Boneh, Jackie Van Ryzin

Research output: Contribution to journalArticle

Abstract

Hit-and-run algorithms are Monte Carlo methods for detecting necessary constraints in convex programming including semidefinite programming. The well known of these in semidefinite programming are semidefinite coordinate directions (SCD), semidefinite hypersphere directions (SHD) and semidefinite stand-and-hit (SSH) algorithms. SCD is considered to be the best on average and hence we use it for comparison. We develop two new hit-and-run algorithms in semidefinite programming that use diagonal directions. They are the uniform semidefinite diagonal directions (uniform SDD) and the original semidefinite diagonal directions (original SDD) algorithms. We analyze the costs and benefits of this change in comparison with SCD. We also show that both uniform SDD and original SDD generate points that are asymptotically uniform in the interior of the feasible region defined by the constraints.

Original languageEnglish (US)
Pages (from-to)2277-2288
Number of pages12
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume14
Issue number5
DOIs
StatePublished - May 1 2009

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Keywords

  • Linear matrix inequalities
  • Monte Carlo method
  • Redundancy
  • Semidefinite programming

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Applied Mathematics

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