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

Title
Generalized lagrangian duals and sums of squares relaxations of sparse polynomial optimization blems
Authors
Kim S.Kojima M.Waki H.
Ewha Authors
김선영
SCOPUS Author ID
김선영scopus
Issue Date
2005
Journal Title
SIAM Journal on Optimization
ISSN
1052-6234JCR Link
Citation
SIAM Journal on Optimization vol. 15, no. 3, pp. 697 - 719
Indexed
SCI; SCIE; SCOPUS WOS scopus
Document Type
Article
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. © 2005 Society for Industrial and Applied Mathematics.
DOI
10.1137/030601260
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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