Noname manuscript No. (will be inserted by the editor) A numerical evaluation of the bounded degree sum-of-squares hierarchy of Lasserre, Toh, and Yang on the pooling problem Ahmadreza Marandi, Joachim Dahl, Etienne de Klerk Received: October 13, 2016/ Accepted: date Abstract The bounded degree sum-of-squares (BSOS) hierarchy of Lasserre, Toh, and Yang [EURO J. Comput. Optim., 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. Keywords sum-of-squares hierarchy, Bilinear optimization, Pooling problem, Semidefinite programming 1. Introduction Polynomial programming is the class of nonlinear optimization problems in- volving polynomials only: A. Marandi Tilburg School of Economics and Management, Tilburg University, The Netherlands E-mail: a.marandi@uvt.nl The research of this author is supported by EU Marie Curie Initial Training Network number 316647 (“Mixed Integer Nonlinear Optimization (MINO)”). J. Dahl MOSEK ApS, Copenhagen O, Denmark E-mail: joachim.dahl@mosek.com E. de Klerk Tilburg School of Economics and Management, Tilburg University, The Netherlands Delft Institute of Applied Mathematics, Delft University of Technology, The Netherlands E-mail: E.deKlerk@uvt.nl