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Semidefinite programming relaxation methods for global optimization problems with sparse polynomials and unbounded semialgebraic feasible sets

Title
Semidefinite programming relaxation methods for global optimization problems with sparse polynomials and unbounded semialgebraic feasible sets
Authors
Jeyakumar, V.Kim, S.Lee, G. M.Li, G.
Ewha Authors
김선영
SCOPUS Author ID
김선영scopus
Issue Date
2016
Journal Title
JOURNAL OF GLOBAL OPTIMIZATION
ISSN
0925-5001JCR Link1573-2916JCR Link
Citation
vol. 65, no. 2, pp. 175 - 190
Keywords
Global continuous optimizationSparse polynomial optimizationStructured sparsitySums of squares polynomialsSemidefinite programming relaxations
Publisher
SPRINGER
Indexed
SCI; SCIE; SCOPUS WOS scopus
Abstract
We propose a hierarchy of semidefinite programming (SDP) relaxations for polynomial optimization with sparse patterns over unbounded feasible sets. The convergence of the proposed SDP hierarchy is established for a class of polynomial optimization problems. This is done by employing known sums-of-squares sparsity techniques of Kojima and Muramatsu Comput Optim Appl 42(1):31-41, (2009) and Lasserre SIAM J Optim 17:822-843, (2006) together with a representation theorem for polynomials over unbounded sets obtained recently in Jeyakumar et al. J Optim Theory Appl 163(3):707-718, (2014). We demonstrate that the proposed sparse SDP hierarchy can solve some classes of large scale polynomial optimization problems with unbounded feasible sets using the polynomial optimization solver SparsePOP developed by Waki et al. ACM Trans Math Softw 35:15 (2008).
DOI
10.1007/s10898-015-0356-6
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자연과학대학 > 수학전공 > Journal papers
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