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

Ahmadreza Marandi (a.marandi***at***uvt.nl)
Joachim Dahl (joachim.dahl***at***mosek.com)
Etienne de Klerk (E.deKlerk***at***uvt.nl)

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

Category 1: Nonlinear Optimization

Category 2: Linear, Cone and Semidefinite Programming (Semi-definite Programming )

Citation:

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Entry Submitted: 05/11/2016
Entry Accepted: 05/11/2016
Entry Last Modified: 10/13/2016

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