Technical communique: On the facet-to-facet property of solutions to convex parametric quadratic programs

  • Authors:

  • JøRgen SpjøTvold;Eric C. Kerrigan;Colin N. Jones;Petter TøNdel;Tor A. Johansen

  • Affiliations:

  • Department of Engineering Cybernetics, Norwegian University of Science and Technology, N-7491 Trondheim, Norway;Department of Aeronautics and Department of Electrical and Electronic Engineering, Imperial College London, Exhibition Road, London SW7 2AZ, UK;Automatic Control Laboratory, ETH-Swiss Federal Institute of Technology, Physikstrasse 3, ETL I 29, CH-8092, Zürich, Switzerland;Department of Engineering Cybernetics, Norwegian University of Science and Technology, N-7491 Trondheim, Norway;Department of Engineering Cybernetics, Norwegian University of Science and Technology, N-7491 Trondheim, Norway

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2006

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Abstract

In some of the recently developed algorithms for convex parametric quadratic programs it is implicitly assumed that the intersection of the closures of two adjacent critical regions is a facet of both closures; this will be referred to as the facet-to-facet property. It is shown by an example, whose solution is unique, that the facet-to-facet property does not hold in general. Consequently, some existing algorithms cannot guarantee that the entire parameter space will be explored. A simple modification, applicable to several existing algorithms, is presented for the purpose of overcoming this problem. Numerical results indicate that, compared to the original algorithms for parametric quadratic programs, the proposed method has lower computational complexity for problems whose solutions consist of a large number of critical regions.