eprintid: 1023
rev_number: 6
eprint_status: archive
dir: disk0/00/00/10/23
datestamp: 2011-12-05 10:20:42
lastmod: 2011-12-05 10:20:42
status_changed: 2011-12-05 10:20:42
type: article
metadata_visibility: show
creators_name: Patrinos, Panagiotis
creators_name: Sarimveis, Haralambos
creators_id: panagiotis.patrinos@imtlucca.it
creators_id: 
title: A new algorithm for solving convex parametric quadratic programs based on graphical derivatives of solution mappings
ispublished: pub
subjects: QA
subjects: QA76
divisions: CSA
full_text_status: none
keywords: Parametric optimization; Algorithms and software; Control of constrained systems
abstract: In this paper we derive formulas for computing graphical derivatives of the (possibly multivalued) solution mapping for convex parametric quadratic programs. Parametric programming has recently received much attention in the control community, however most algorithms are based on the restrictive assumption that the so called critical regions of the solution form a polyhedral subdivision, i.e. the intersection of two critical regions is either empty or a face of both regions. Based on the theoretical results of this paper, we relax this assumption and show how we can efficiently compute all adjacent full dimensional critical regions along a facet of an already discovered critical region. Coupling the proposed approach with the graph traversal paradigm, we obtain very efficient algorithms for the solution of parametric convex quadratic programs
date: 2010-09
date_type: published
publication: Automatica
volume: 46
number: 9
publisher: Elsevier 
pagerange: 1405-1418
id_number: 10.1016/j.automatica.2010.06.008
refereed: TRUE
issn: 0005-1098
official_url: http://www.sciencedirect.com/science/article/pii/S000510981000258X
citation:   Patrinos, Panagiotis and Sarimveis, Haralambos  A new algorithm for solving convex parametric quadratic programs based on graphical derivatives of solution mappings.  Automatica, 46 (9).  pp. 1405-1418.  ISSN 0005-1098      (2010)