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

Journal article (2018)

Authors

Ahmadreza Marandi Tilburg University
Joachim Dahl MOSEK ApS
E. de Klerk Tilburg University, Discrete Mathematics and Optimization - EEMCS
Research Group
Discrete Mathematics and Optimization (EEMCS) (TU Delft)
Copyright: © 2018 Ahmadreza Marandi, Joachim Dahl, E. de Klerk
DOI
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https://doi.org/10.1007/s10479-017-2407-5
Semidefinite programming Bilinear optimization Pooling problem Sum-of-squares hierarchy
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Published Date

2018

Language

English

Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Discrete Mathematics and Optimization

Abstract

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.