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

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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
StatePublished - 22 Apr 2018

    Research areas

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

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