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Unconstrained and inequality constrained sparse polynomial optimization problems (POPs) are considered. A correlative sparsity pattern graph is defined to find a certain sparse structure in the objective and constraint polynomials of a POP. Based on this graph, sets of supports for sums of squares (SOS) polynomials that lead to efficient SOS and… (More)

We propose a new relaxation scheme for the MAX-CUT problem using second-order cone programming. We construct relaxation problems to reflect the structure of the original graph. Numerical experiments show that our relaxation gives better bounds than those based on the spectral decomposition proposed by Kim and Kojima [16], and that the efficiency of the… (More)

SparesPOP is a MATLAB implementation of a sparse semidefinite programming (SDP) relaxation method proposed for polynomial optimization problems (POPs) in the recent paper by Waki et al. The sparse SDP relaxation is based on " a hierarchy of LMI relaxations of increasing dimensions " by Lasserre, and exploits a sparsity structure of polynomials in POPs. The… (More)

SparsePOP is a Matlab implementation of the sparse semidefinite programming (SDP) relaxation method for approximating a global optimal solution of a polynomial optimization problem (POP) proposed by Waki et al. [2006]. The sparse SDP relaxation exploits a sparse structure of polynomials in POPs when applying “a hierarchy of LMI relaxations of… (More)

To obtain a primal-dual pair of conic programming problems having zero duality gap, two methods have been proposed: the facial reduction algorithm due to Borwein and Wolkowicz [1, 2] and the conic expansion method due to Luo, Sturm, and Zhang [5]. We establish a clear relationship between them. Our results show that although the two methods can be regarded… (More)

This paper is based on a recent work by Kojima which extended sums of squares relaxations of polynomial optimization problems to polynomial semidefinite programs. Let E and E + be a finite dimensional real vector space and a symmetric cone embedded in E; examples of E and E + include a pair of the N-dimensional Euclidean space and its nonnegative orthant, a… (More)