Location of Repository

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

By P. M. Kleniati, Panos Parpas and 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] .Polynomial optimization, Semidefinite programming, Sparse SDP relaxations, Benders decomposition

OAI identifier:

Suggested articles

Preview

Citations

  1. (1990). A collection of test problems for constrained global optimization algorithms,
  2. (2005). A conic interior point decomposition approach for large scale semidefinite programming,
  3. (2001). A log-barrier method with Benders decomposition for solving two-stage stochastic linear programs.
  4. (1999). A note on feasibility in benders decomposition,
  5. (2008). A parallel interior point decomposition algorithm for block angular semidefinite programs. Computational Optimization and Applications,
  6. (1996). An interior point method for semidefinite programming.
  7. (2006). Convergent SDP-Relaxations in Polynomial Optimization with Sparsity.
  8. (1999). CSDP, A C library for semidefinite programming.
  9. (1999). Cuts and semidefinite relaxations for nonconvex quadratic problems.
  10. (2009). Decomposition Schemes for Polynomial Optimization, Semidefinite Programming and Applications to Nonconvex Portfolio Decisions.
  11. (2005). DSDP5: Software for semidefinite programming.
  12. (1998). editors. Topics in semidefinite and interior-point methods,
  13. (1972). Generalized Benders decomposition.
  14. Global optimization with polynomials and the problem of moments.
  15. (1995). Interior point methods in semidefinite programming with applications to combinatorial optimization.
  16. (2005). Moment matrices and optimization over polynomials,
  17. (2005). Partitioning procedures for solving mixed-variables programming problems.
  18. (2006). Recognizing underlying sparsity in optimization.
  19. (2003). Semidefinite programming relaxations for semialgebraic problems.
  20. (1996). Semidefinite programming. In Interior point methods of mathematical programming,
  21. (1995). Some geometric results in semidefinite programming.
  22. (2006). Sums of squares and semidefinite program relaxations for polynomial optimization problems with structured sparsity.
  23. (2000). The geometry of semidefinite programming. In Handbook of semidefinite programming,
  24. (2006). User Guide for CHOLMOD: a sparse Cholesky factorization and modification package.
  25. (1999). Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones. Optimization Methods and Software,

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.