Convergent SDP-Relaxations for Polynomial Optimization with Sparsity
We consider a polynomial programming problem P on a compact basic semi-algebraic set K ⊂ ℝ n , described by m polynomial inequalities g j (X)≥0, and with criterion f ∈ ℝ[X]. We propose a hierarchy of semidefinite relaxations that take sparsity of the original data into account, in the spirit of those of Waki et al. . The novelty with respect to  is that we prove convergence to the global optimum of P when the sparsity pattern satisfies a condition often encountered in large size problems of practical applications, and known as the running intersection property in graph theory.
KeywordsChordal Graph Sparsity Pattern Matrix Completion Polynomial Optimization Polynomial Optimization Problem
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