A numerical evaluation of the bounded degree sum-of-squares hierarchy of Lasserre, Toh, and Yang on the pooling problem

The bounded degree sum-of-squares (BSOS) hierarchy of Lasserre et al. (EURO J Comput Optim 1–31, 2015) constructs lower bounds for a general polynomial optimization problem with compact feasible set, by solving a sequence of semi-definite programming (SDP) problems. Lasserre, Toh, and Yang prove that these lower bounds converge to the optimal value of the original problem, under some assumptions. In this paper, we analyze the BSOS hierarchy and study its numerical performance on a specific class of bilinear programming problems, called pooling problems, that arise in the refinery and chemical process industries.