### Abstract

Original language | English |
---|---|

Pages (from-to) | 67-92 |

Journal | Annals of Operations Research |

Volume | 265 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jun 2018 |

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### Keywords

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

### Cite this

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*Annals of Operations Research*, vol. 265, no. 1, pp. 67-92. https://doi.org/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.** / Marandi, Ahmadreza; Dahl, Joachim; de Klerk, Etienne.

Research output: Contribution to journal › Article › Scientific › peer-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, Ahmadreza

AU - Dahl, Joachim

AU - de Klerk, Etienne

PY - 2018/6

Y1 - 2018/6

N2 - 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.

AB - 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.

KW - sum-of-squares hierarchy

KW - Bilinear optimization

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

JF - Annals of Operations Research

SN - 0254-5330

IS - 1

ER -