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EXACT SEMIDEFINITE PROGRAMMING RELAXATIONS WITH TRUNCATED MOMENT MATRIX FOR BINARY POLYNOMIAL OPTIMIZATION PROBLEMS

Title
EXACT SEMIDEFINITE PROGRAMMING RELAXATIONS WITH TRUNCATED MOMENT MATRIX FOR BINARY POLYNOMIAL OPTIMIZATION PROBLEMS
Authors
Sakaue, ShinsakuTakeda, AkikoKim, SunyoungIto, Naoki
Ewha Authors
김선영
SCOPUS Author ID
김선영scopus
Issue Date
2017
Journal Title
SIAM JOURNAL ON OPTIMIZATION
ISSN
1052-6234JCR Link1095-7189JCR Link
Citation
vol. 27, no. 1, pp. 565 - 582
Keywords
binary polynomial optimization problemshierarchy of SDP relaxationsbound for the exact SDP relaxationeven-degree binary polynomial optimization problemschordal graph
Publisher
SIAM PUBLICATIONS
Indexed
SCI; SCIE; SCOPUS WOS
Abstract
For binary polynomial optimization problems (POPs) of degree d with n variables, we prove that the [(n+d-1)/2]th semidefinite programming (SDP) relaxation in Lasserre's hierarchy of SDP relaxations provides the exact optimal value. If binary POPs involve only even-degree monomials, we show that it can be further reduced to [(n+d-2)/2]. This bound on the relaxation order coincides with the conjecture by Laurent in 2003, which was recently proved by Fawzi, Saunderson, and Parrilo, on binary quadratic optimization problems where d = 2. We also numerically confirm that the bound is tight. More precisely, we present instances of binary POPs that require solving at least the [(n+d-1)/2]th SDP relaxation for general binary POPs and the [(n+d-2)/2]th SDP relaxation for even-degree binary POPs to obtain the exact optimal values.
DOI
10.1137/16M105544X
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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