https://hal-supelec.archives-ouvertes.fr/hal-00827224Feller, ChristianChristianFellerUniversity of StuttgartArne Johansen, TorTorArne JohansenNTNU - Norwegian University of Science and Technology [Trondheim] - NTNU - Norwegian University of Science and TechnologyOlaru, SorinSorinOlaruE3S - Supélec Sciences des Systèmes - Ecole Supérieure d'Electricité - SUPELEC (FRANCE)An improved algorithm for combinatorial multi-parametric quadratic programmingHAL CCSD2013[SPI.AUTO] Engineering Sciences [physics]/AutomaticDartron, Josiane2013-05-29 09:11:542021-02-23 19:24:062013-05-29 13:44:15enJournal articles10.1016/j.automatica.2013.02.0221The goal of multi-parametric quadratic programming (mpQP) is to compute analytic solutions to parameter-dependent constrained optimization problems, e.g., in the context of explicit linear MPC. We propose an improved combinatorial mpQP algorithm that is based on implicit enumeration of all possible optimal active sets and a simple saturation matrix pruning criterion which uses geometric properties of the constraint polyhedron for excluding infeasible candidate active sets. In addition, techniques are presented that allow to reduce the complexity of the discussed algorithm in the presence of symmetric problem constraints. Performance improvements are discussed for two example problems from the area of explicit linear MPC.