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Amir Ali Ahmadi (a_a_aprinceton.edu) Abstract: We devise a scheme for solving an iterative sequence of linear programs (LPs) or second order cone programs (SOCPs) to approximate the optimal value of any semidefinite program (SDP) or sum of squares (SOS) program. The first LP and SOCPbased bounds in the sequence come from the recent work of Ahmadi and Majumdar on diagonally dominant sum of squares (DSOS) and scaled diagonally dominant sum of squares (SDSOS) polynomials. We then iteratively improve on these bounds by pursuing better bases in which more relevant SOS polynomials admit a DSOS or SDSOS representation. Different interpretations of the procedure from primal and dual perspectives are given. While the approach is applicable to SDP relaxations of general polynomial programs, we apply it to two problems of discrete optimization: the maximum independent set problem and the partition problem. We further show that some completely trivial instances of the partition problem lead to strictly positive polynomials on the boundary of the sum of squares cone and hence make the SOS relaxation fail. Keywords: Category 1: Linear, Cone and Semidefinite Programming Category 2: Combinatorial Optimization (Approximation Algorithms ) Category 3: Nonlinear Optimization Citation: ORFE, Sherrerd Hall, Princeton University, Princeton, NJ 08540 ; October 2015 Download: [PDF] Entry Submitted: 10/09/2015 Modify/Update this entry  
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