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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

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] .

Suggested Citation

  • P. M. Kleniati & Panos Parpas & Berc Rustem, 2009. "Decomposition-Based Method for Sparse Semidefinite Relaxations of Polynomial Optimization Problems," Working Papers 022, COMISEF.
  • Handle: RePEc:com:wpaper:022
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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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    Keywords

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

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