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

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.
LanguageEnglish
Pages67-92
JournalAnnals of Operations Research
Volume265
Issue number1
DOIs
StatePublished - Jun 2018

Fingerprint

Evaluation
Pooling
Lower bounds
Optimization problem
Programming
Semidefinite programming
Process industry
Refinery
Polynomials

Keywords

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

Cite this

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A numerical evaluation of the bounded degree sum-of-squares hierarchy of Lasserre, Toh, and Yang on the pooling problem. / Marandi, Ahmadreza; Dahl, Joachim; de Klerk, Etienne.

In: Annals of Operations Research, Vol. 265, No. 1, 06.2018, p. 67-92.

Research output: Contribution to journalArticleScientificpeer-review

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