Partitioning procedure for polynomial optimization

Authors:
Polyxeni-Margarita Kleniati;Panos Parpas;Berç Rustem
Affiliations:
Department of Computing, Imperial College London, London, UK SW7 2AZ;Energy Initiative Engineering Systems Division, Massachusetts Institute of Technology, Cambridge, UK 02139;Department of Computing, Imperial College London, London, UK SW7 2AZ
Venue:
Journal of Global Optimization
Year:
2010

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Abstract

We consider the problem of finding the minimum of a real-valued multivariate polynomial function constrained in a compact set defined by polynomial inequalities and equalities. This problem, called polynomial optimization problem (POP), is generally nonconvex and has been of growing interest to many researchers in recent years. Our goal is to tackle POPs using decomposition, based on a partitioning procedure. The problem manipulations are in line with the pattern used in the generalized Benders decomposition, namely projection followed by relaxation. Stengle's and Putinar's Positivstellensätze are employed to derive the feasibility and optimality constraints, respectively. We test the performance of the proposed partitioning procedure on a collection of benchmark problems and present the numerical results.