Decomposition-based Method for Sparse Semidefinite Relaxations of Polynomial Optimization Problems

P. M. Kleniati (), P. Parpas and B. Rustem
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P. M. Kleniati: Imperial College London
P. Parpas: Imperial College London
B. Rustem: Imperial College London

Journal of Optimization Theory and Applications, 2010, vol. 145, issue 2, No 5, 289-310

Abstract: Abstract We consider polynomial optimization problems pervaded by a sparsity pattern. It has been shown in Lasserre (SIAM J. Optim. 17(3):822–843, 2006) and Waki et al. (SIAM J. Optim. 17(1):218–248, 2006) that the optimal solution of a polynomial programming problem with structured sparsity can be computed by solving a series of semidefinite relaxations that possess the same kind of sparsity. We aim at solving the former relaxations with a decomposition-based method, which partitions the relaxations according to their sparsity pattern. The decomposition-based method that we propose is an extension to semidefinite programming of the Benders decomposition for linear programs (Benders, Comput. Manag. Sci. 2(1):3–19, 2005).

Keywords: Polynomial optimization; Semidefinite programming; Sparse SDP relaxations; Benders decomposition (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/s10957-009-9624-2

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