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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

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

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