An extension of the elimination method for a sparse sos polynomial

Hayato Waki, Masakazu Muramatsu

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We propose a method to reduce the sizes of SDP relaxation problems fur a given polynomial optimization problem (POP). This method is an extension of the elimination method for a sparse SOS polynomial in [8] and exploits sparsity of polynomials involved in a given POP. In addition, we show that this method is a partial application of a facial reduction algorithm, which generates a smaller SDP problem with an interior feasible solution. In general, SDP relaxation problems for POPs often become highly degenerate because of a lack of interior feasible solutions. As a result, the resulting SDP relaxation problems obtained by this method may have an interior feasible solution, and one may be able to solve the SDP relaxation problems effectively Numerical results in this paper show that the resulting SDP relaxation problems obtained by this method can be solved fast and accurately.

Original languageEnglish
Pages (from-to)161-190
Number of pages30
JournalJournal of the Operations Research Society of Japan
Volume54
Issue number4
DOIs
Publication statusPublished - Dec 2011
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Decision Sciences(all)
  • Management Science and Operations Research

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