Solving sparse polynomial optimization problems with chordal structure using the sparse, bounded-degree sum-of-squares hierarchy

The sparse bounded degree sum-of-squares (sparse-BSOS) hierarchy of Weisser, Lasserre, and Toh [arXiv:1607.01151,2016] constructs a sequence of lower bounds for a sparse polynomial optimization problem. Under some assumptions, it is proven by the authors that the sequence converges to the optimal value. In this paper, we modify the hierarchy to deal with problems containing equality constraints directly, without eliminating or replacing them by two inequalities. We also evaluate the sparse-BSOS hierarchy on a well-known bilinear programming problem, called the pooling problem