Sparse-BSOS: a bounded degree SOS hierarchy for large scale polynomial optimization with sparsity
Optimization and Control
2017-05-30 v3
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.
Cite
@article{arxiv.1607.01151,
title = {Sparse-BSOS: a bounded degree SOS hierarchy for large scale polynomial optimization with sparsity},
author = {Tillmann Weisser and Jean-Bernard Lasserre and Kim-Chuan Toh},
journal= {arXiv preprint arXiv:1607.01151},
year = {2017}
}