View : 18 Download: 0
EXACT SEMIDEFINITE PROGRAMMING RELAXATIONS WITH TRUNCATED MOMENT MATRIX FOR BINARY POLYNOMIAL OPTIMIZATION PROBLEMS
- EXACT SEMIDEFINITE PROGRAMMING RELAXATIONS WITH TRUNCATED MOMENT MATRIX FOR BINARY POLYNOMIAL OPTIMIZATION PROBLEMS
- Sakaue, Shinsaku; Takeda, Akiko; Kim, Sunyoung; Ito, Naoki
- Ewha Authors
- SCOPUS Author ID
- Issue Date
- Journal Title
- SIAM JOURNAL ON OPTIMIZATION
- 1052-6234; 1095-7189
- vol. 27, no. 1, pp. 565 - 582
- binary polynomial optimization problems; hierarchy of SDP relaxations; bound for the exact SDP relaxation; even-degree binary polynomial optimization problems; chordal graph
- SIAM PUBLICATIONS
- SCI; SCIE; SCOPUS
- 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.
- Appears in Collections:
- 자연과학대학 > 수학전공 > Journal papers
- Files in This Item:
There are no files associated with this item.
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.