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

Author

Listed:
  • P. M. Kleniati

    (Imperial College London)

  • P. Parpas

    (Imperial College London)

  • B. Rustem

    (Imperial College London)

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).

Suggested Citation

  • P. M. Kleniati & P. Parpas & B. Rustem, 2010. "Decomposition-based Method for Sparse Semidefinite Relaxations of Polynomial Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 145(2), pages 289-310, May.
    • Handle: RePEc:spr:joptap:v:145:y:2010:i:2:d:10.1007_s10957-009-9624-2
    DOI: 10.1007/s10957-009-9624-2
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    References listed on IDEAS

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    1. Laurent, M., 2009. "Sums of squares, moment matrices and optimization over polynomials," Other publications TiSEM 9fef820b-69d2-43f2-a501-e, Tilburg University, School of Economics and Management.
    2. J. Benders, 2005. "Partitioning procedures for solving mixed-variables programming problems," Computational Management Science, Springer, vol. 2(1), pages 3-19, January.
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    Cited by:

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