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

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 and efficient modification, applicable to several existing algorithms, is presented for the purpose of overcoming this problem. Key words: Parametric programming. Quadratic programming. Explicit model predictive control.

• Type: Journal
• Year: 2006
• Where: AUTOMATICA
• Authors: Jørgen Spjøtvold, Eric C. Kerrigan, Colin Neil Jones, Petter Tøndel, Tor Arne Johansen
• Keywords: Adjacent Critical Regions, AUTOMATICA 2006, Facet-to-facet Property, Parametric Quadratic Programs