Generalized lagrangian duals and sums of squares relaxations of sparse polynomial optimization blems

Sunyoung Kim, Masakazu Kojima, Hayato Waki

Research output: Contribution to journalArticle

41 Citations (Scopus)

Abstract

Sequences of generalized Lagrangian duals and their sums of squares (SOS) of polynomials relaxations for a polynomial optimization problem (POP) are introduced. The sparsity of polynomials in the POP is used to reduce the sizes of the Lagrangian duals and their SOS relaxations. It is proved that the optimal values of the Lagrangian duals in the sequence converge to the optimal value of the POP using a method from the penalty function approach. The sequence of SOS relaxations is transformed into a sequence of semidefinite programing (SDP) relaxations of the POP, which correspond to duals of modification and generalization of SDP relaxations given by Lasserre for the POP.

Original languageEnglish
Pages (from-to)697-719
Number of pages23
JournalSIAM Journal on Optimization
Volume15
Issue number3
DOIs
Publication statusPublished - Aug 26 2005
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Software
  • Theoretical Computer Science

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