Characterization of strong stability for C-stationary points in MPCC

Authors:
H. Th. Jongen;V. Shikhman;S. Steffensen
Affiliations:
RWTH Aachen University, Department of Mathematics–C, 52056, Aachen, Germany;RWTH Aachen University, Department of Mathematics–C, 52056, Aachen, Germany;RWTH Aachen University, Department of Mathematics–C, 52056, Aachen, Germany
Venue:
Mathematical Programming: Series A and B
Year:
2012

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The C-Index: A New Stability Concept for Quadratic Programs with Complementarity Constraints

Mathematics of Operations Research

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Abstract

We study mathematical programs with complementarity constraints (MPCC). Special focus will be on C-stationary points. Under the Linear Independence Constraint Qualification we characterize strong stability of C-stationary points (in the sense of Kojima) by means of first and second order information of the defining functions. It turns out that strong stability of C-stationary points allows a possible degeneracy of bi-active Lagrange multipliers. Some relations to other stationarity concepts (such as A-, M-, S- and B-stationarity) are shortly discussed.