3 years ago

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

Kim-Chuan Toh, Jean B. Lasserre, Tillmann Weisser

Abstract

We provide a sparse version of the bounded degree SOS hierarchy BSOS (Lasserre et al. in EURO J Comp Optim:87–117, 2017) 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.

Publisher URL: https://link.springer.com/article/10.1007/s12532-017-0121-6

DOI: 10.1007/s12532-017-0121-6

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