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

Title

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

 Author

Marandi, Ahmadreza (Tilburg University)
Dahl, Joachim (MOSEK ApS)
de Klerk, E. (TU Delft Optimization; Tilburg University)

Date

2018

 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.


 Subject

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

 To reference this document use:

http://resolver.tudelft.nl/uuid:027e74dd-0f02-4d8f-bbf8-52d7f22ceb13

 DOI

https://doi.org/10.1007/s10479-017-2407-5

 ISSN

0254-5330

 Source

Annals of Operations Research, 265, 67-92

 Part of collection

Institutional Repository

 Document type

journal article

 Rights

© 2018 Ahmadreza Marandi, Joachim Dahl, E. de Klerk
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