TY  - JOUR
VL  - 46
Y1  - 2010/09//
IS  - 9
JF  - Automatica
A1  - Patrinos, Panagiotis
A1  - Sarimveis, Haralambos
PB  - Elsevier 
SP  - 1405
ID  - eprints1023
EP  - 1418
AV  - none
TI  - A new algorithm for solving convex parametric quadratic programs based on graphical derivatives of solution mappings
KW  - Parametric optimization; Algorithms and software; Control of constrained systems
UR  - http://www.sciencedirect.com/science/article/pii/S000510981000258X
SN  - 0005-1098
N2  - 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
ER  -