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

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  • P. M. Kleniati
  • Panos Parpas
  • Berc Rustem
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    Abstract

    We 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 [3] .

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    File URL: http://comisef.eu/files/wps022.pdf
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    Bibliographic Info

    Paper provided by COMISEF in its series Working Papers with number 022.

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    Length: 29 pages
    Date of creation: 10 Nov 2009
    Date of revision:
    Handle: RePEc:com:wpaper:022

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    Web page: http://www.comisef.eu

    Related research

    Keywords: Polynomial optimization; Semidefinite programming; Sparse SDP relaxations; Benders decomposition;

    This paper has been announced in the following NEP Reports:

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    Cited by:
    1. 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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