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
Pages (from-to)95-110
JournalDiscrete Applied Mathematics
Volume275
DOIs
Publication statusPublished - Mar 2020

Keywords

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

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