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

A. Marandi; E. de Klerk; J. Dahl

doi:10.1007/s10479-017-2407-5

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

A. Marandi, E. de Klerk, J. Dahl

Research output: Contribution to journal › Article › Academic › peer-review

7 Citations (Scopus)

116 Downloads (Pure)

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.

Original language	English
Pages (from-to)	67-92
Number of pages	26
Journal	Annals of Operations Research
Volume	265
Issue number	1
DOIs	https://doi.org/10.1007/s10479-017-2407-5
Publication status	Published - 1 Jun 2018
Externally published	Yes

Keywords

Sum-of-squares hierarchy
Bilinear Programming
Pooling Problem
Semidefinite Programming
Bilinear optimization
Pooling problem
Semidefinite programming

Access to Document

10.1007/s10479-017-2407-5

published versionFinal published version, 492 KB

Cite this

@article{11dea618384c4fe189ed0774354649d7,

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

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.",

keywords = "Sum-of-squares hierarchy, Bilinear Programming, Pooling Problem, Semidefinite Programming, Bilinear optimization, Pooling problem, Semidefinite programming",

author = "A. Marandi and {de Klerk}, E. and J. Dahl",

year = "2018",

month = jun,

day = "1",

doi = "10.1007/s10479-017-2407-5",

language = "English",

volume = "265",

pages = "67--92",

journal = "Annals of Operations Research",

issn = "0254-5330",

publisher = "Springer",

number = "1",

}

TY - JOUR

T1 - A numerical evaluation of the bounded degree sum-of-squares hierarchy of Lasserre, Toh, and Yang on the pooling problem

AU - Marandi, A.

AU - de Klerk, E.

AU - Dahl, J.

PY - 2018/6/1

Y1 - 2018/6/1

N2 - 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.

AB - 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.

KW - Sum-of-squares hierarchy

KW - Bilinear Programming

KW - Pooling Problem

KW - Semidefinite Programming

KW - Bilinear optimization

KW - Pooling problem

KW - Semidefinite programming

UR - http://www.scopus.com/inward/record.url?scp=85011691158&partnerID=8YFLogxK

U2 - 10.1007/s10479-017-2407-5

DO - 10.1007/s10479-017-2407-5

M3 - Article

SN - 0254-5330

VL - 265

SP - 67

EP - 92

JO - Annals of Operations Research

JF - Annals of Operations Research

IS - 1

ER -

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

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this