Lipschitz continuity of solutions of linear inequalities, programs and complementarity problems
SIAM Journal on Control and Optimization
Convergence behavior of interior-point algorithms
Mathematical Programming: Series A and B
Directional derivatives of the solution of a parametric nonlinear program
Mathematical Programming: Series A and B
Variational conditions and the proto-differentiation of partial subgradient mappings
Nonlinear Analysis: Theory, Methods & Applications
Solution Sensitivity from General Principles
SIAM Journal on Control and Optimization
Ample Parameterization of Variational Inclusions
SIAM Journal on Optimization
Automatica (Journal of IFAC)
Multiobjective model predictive control
Automatica (Journal of IFAC)
Automatica (Journal of IFAC)
Primal-dual enumeration for multiparametric linear programming
ICMS'06 Proceedings of the Second international conference on Mathematical Software
The explicit linear quadratic regulator for constrained systems
Automatica (Journal of IFAC)
Brief An algorithm for multi-parametric quadratic programming and explicit MPC solutions
Automatica (Journal of IFAC)
Computation of the constrained infinite time linear quadratic regulator
Automatica (Journal of IFAC)
A simple characterization of solution sets of convex programs
Operations Research Letters
Brief paper: Convex parametric piecewise quadratic optimization: Theory and algorithms
Automatica (Journal of IFAC)
Hi-index | 22.15 |
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.