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

Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

3 Citaties (Scopus)

Uittreksel

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.
TaalEngels
Pagina's67-92
TijdschriftAnnals of Operations Research
Volume265
Nummer van het tijdschrift1
DOI's
StatusGepubliceerd - 2018
Extern gepubliceerdJa

Vingerafdruk

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

Trefwoorden

    Citeer dit

    @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",
    author = "A. Marandi and {de Klerk}, E. and J. Dahl",
    year = "2018",
    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",

    }

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

    In: Annals of Operations Research, Vol. 265, Nr. 1, 2018, blz. 67-92.

    Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

    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

    Y1 - 2018

    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

    U2 - 10.1007/s10479-017-2407-5

    DO - 10.1007/s10479-017-2407-5

    M3 - Article

    VL - 265

    SP - 67

    EP - 92

    JO - Annals of Operations Research

    T2 - Annals of Operations Research

    JF - Annals of Operations Research

    SN - 0254-5330

    IS - 1

    ER -