Solving Sparse Polynomial Optimization Problems with Chordal Structure Using the Sparse, Bounded-Degree Sum-of-Squares Hierarchy

Ahmadreza Marandi, Etienne de Klerk, Joachim Dahl

Research output: Working paperDiscussion paperOther research output

Abstract

The sparse bounded degree sum-of-squares (sparse-BSOS) hierarchy of Weisser, Lasserre and Toh [arXiv:1607.01151,2016] constructs a sequence of lower bounds for a sparse polynomial optimization problem. Under some assumptions, it is proven 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.
LanguageEnglish
PublisherOptimization Online
StatePublished - May 2017

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Polynomials

Keywords

  • Polynomial optimization
  • Sparse sum-of-squares hierarchy
  • Semi-definite programming
  • Pooling problem
  • Chordal sparsity structure

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, Lasserre and Toh [arXiv:1607.01151,2016] constructs a sequence of lower bounds for a sparse polynomial optimization problem. Under some assumptions, it is proven 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.",
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author = "Ahmadreza Marandi and {de Klerk}, Etienne and Joachim Dahl",
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language = "English",
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Solving Sparse Polynomial Optimization Problems with Chordal Structure Using the Sparse, Bounded-Degree Sum-of-Squares Hierarchy. / Marandi, Ahmadreza; de Klerk, Etienne; Dahl, Joachim.

Optimization Online, 2017.

Research output: Working paperDiscussion paperOther research output

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AU - de Klerk,Etienne

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N2 - The sparse bounded degree sum-of-squares (sparse-BSOS) hierarchy of Weisser, Lasserre and Toh [arXiv:1607.01151,2016] constructs a sequence of lower bounds for a sparse polynomial optimization problem. Under some assumptions, it is proven 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.

AB - The sparse bounded degree sum-of-squares (sparse-BSOS) hierarchy of Weisser, Lasserre and Toh [arXiv:1607.01151,2016] constructs a sequence of lower bounds for a sparse polynomial optimization problem. Under some assumptions, it is proven 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.

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KW - Sparse sum-of-squares hierarchy

KW - Semi-definite programming

KW - Pooling problem

KW - Chordal sparsity structure

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PB - Optimization Online

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