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

Ahmadreza Marandi(A.marandi***at***uvt.nl)
Etienne de Klerk(e.deklerk***at***uvt.nl)
Joachim Dahl(joachim.dahl***at***mosek.com)

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.

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

Category 1: Global Optimization

Category 2: Nonlinear Optimization (Quadratic Programming )

Category 3: Linear, Cone and Semidefinite Programming (Semi-definite Programming )


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Entry Submitted: 03/05/2017
Entry Accepted: 03/06/2017
Entry Last Modified: 03/05/2017

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