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

Research output: Contribution to journalArticleScientificpeer-review

5 Citations (Scopus)
127 Downloads (Pure)

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.
Original languageEnglish
Pages (from-to)67-92
JournalAnnals of Operations Research
Volume265
Issue number1
DOIs
Publication statusPublished - Jun 2018

Keywords

  • sum-of-squares hierarchy
  • Bilinear optimization
  • Pooling problem
  • Semidefinite programming

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