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arXiv · 1607.01151

Sparse-BSOS: a bounded degree SOS hierarchy for large scale polynomial optimization with sparsity

Tillmann Weisser·Jean-Bernard Lasserre·Kim-Chuan Toh
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Abstract

We provide a sparse version of the bounded degree SOS hierarchy BSOS [7] for polynomial optimization problems. It permits to treat large scale problems which satisfy a structured sparsity pattern. When the sparsity pattern satisfies the running intersection property this Sparse-BSOS hierarchy of semidefinite programs (with semidefinite constraints of fixed size) converges to the global optimum of the original problem. Moreover, for the class of SOS-convex problems, finite convergence takes place at the first step of the hierarchy, just as in the dense version.

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Tillmann Weisser, Jean-Bernard Lasserre, Kim-Chuan Toh. 2016-07-05. Sparse-BSOS: a bounded degree SOS hierarchy for large scale polynomial optimization with sparsity. https://arxiv.org/abs/1607.01151

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