Decomposition-Based Method for Sparse Semidefinite Relaxations of Polynomial Optimization Problems
AbstractWe consider polynomial optimization problems pervaded by a sparsity pattern. It has been shown in [1, 2] 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 decompositionbased 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  .
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Bibliographic InfoPaper provided by COMISEF in its series Working Papers with number 022.
Length: 29 pages
Date of creation: 10 Nov 2009
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Web page: http://www.comisef.eu
Polynomial optimization; Semidefinite programming; Sparse SDP relaxations; Benders decomposition;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2009-12-05 (All new papers)
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- Polyxeni-Margarita Kleniati & Panos Parpas & Berç Rustem, 2010. "Partitioning procedure for polynomial optimization," Journal of Global Optimization, Springer, vol. 48(4), pages 549-567, December.
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