Journal of Global Optimization

, Volume 48, Issue 4, pp 549–567

Partitioning procedure for polynomial optimization

  • Polyxeni-Margarita Kleniati
  • Panos Parpas
  • Berç Rustem
Article

DOI: 10.1007/s10898-010-9529-5

Cite this article as:
Kleniati, PM., Parpas, P. & Rustem, B. J Glob Optim (2010) 48: 549. doi:10.1007/s10898-010-9529-5

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.

Keywords

Polynomial optimization Positivstellensatz Sum of squares Benders decomposition 

Copyright information

© Springer Science+Business Media, LLC. 2010

Authors and Affiliations

  • Polyxeni-Margarita Kleniati
    • 1
  • Panos Parpas
    • 2
  • Berç Rustem
    • 1
  1. 1.Department of ComputingImperial College LondonLondonUK
  2. 2.Energy Initiative Engineering Systems DivisionMassachusetts Institute of TechnologyCambridgeUK

Personalised recommendations