Solving sparse polynomial optimization problems with chordal structure using the sparse bounded-degree sum-of-squares hierarchy

Etienne de Klerk, Ahmadreza Marandi, Joachim Dahl

Research output: Contribution to journalArticleScientificpeer-review

Abstract

The sparse bounded degree sum-of-squares (sparse-BSOS) hierarchy of Weisser et al. (2017) constructs a sequence of lower bounds for a sparse polynomial optimization problem. Under some assumptions, it is proved by the authors that the sequence converges to the optimal value. In this paper, we modify the hierarchy to deal with problems containing equality constraints directly, without eliminating or replacing them by two inequalities. We also evaluate the sparse-BSOS hierarchy on a well-known bilinear programming problem, called the pooling problem, as well as a discrete-time optimal control problem.
Original languageEnglish
JournalDiscrete Applied Mathematics
DOIs
Publication statusE-pub ahead of print - 2018

Fingerprint

Sparse Polynomials
Degree Sum
Sum of squares
Polynomials
Optimization Problem
Bilinear Programming
Pooling
Equality Constraints
Optimal Control Problem
Discrete-time
Lower bound
Converge
Evaluate
Hierarchy

Keywords

  • polynomial optimization
  • sparse sum-of-squares hierarchy
  • semi-definite programming
  • pooling problem
  • chordal sparsity structure
  • discrete-time optimal control

Cite this

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title = "Solving sparse polynomial optimization problems with chordal structure using the sparse bounded-degree sum-of-squares hierarchy",
abstract = "The sparse bounded degree sum-of-squares (sparse-BSOS) hierarchy of Weisser et al. (2017) constructs a sequence of lower bounds for a sparse polynomial optimization problem. Under some assumptions, it is proved by the authors that the sequence converges to the optimal value. In this paper, we modify the hierarchy to deal with problems containing equality constraints directly, without eliminating or replacing them by two inequalities. We also evaluate the sparse-BSOS hierarchy on a well-known bilinear programming problem, called the pooling problem, as well as a discrete-time optimal control problem.",
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year = "2018",
doi = "10.1016/j.dam.2017.12.015",
language = "English",
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Solving sparse polynomial optimization problems with chordal structure using the sparse bounded-degree sum-of-squares hierarchy. / de Klerk, Etienne; Marandi, Ahmadreza; Dahl, Joachim.

In: Discrete Applied Mathematics, 2018.

Research output: Contribution to journalArticleScientificpeer-review

TY - JOUR

T1 - Solving sparse polynomial optimization problems with chordal structure using the sparse bounded-degree sum-of-squares hierarchy

AU - de Klerk, Etienne

AU - Marandi, Ahmadreza

AU - Dahl, Joachim

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AB - The sparse bounded degree sum-of-squares (sparse-BSOS) hierarchy of Weisser et al. (2017) constructs a sequence of lower bounds for a sparse polynomial optimization problem. Under some assumptions, it is proved by the authors that the sequence converges to the optimal value. In this paper, we modify the hierarchy to deal with problems containing equality constraints directly, without eliminating or replacing them by two inequalities. We also evaluate the sparse-BSOS hierarchy on a well-known bilinear programming problem, called the pooling problem, as well as a discrete-time optimal control problem.

KW - polynomial optimization

KW - sparse sum-of-squares hierarchy

KW - semi-definite programming

KW - pooling problem

KW - chordal sparsity structure

KW - discrete-time optimal control

U2 - 10.1016/j.dam.2017.12.015

DO - 10.1016/j.dam.2017.12.015

M3 - Article

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

ER -