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

We introduce nondegeneracy and the C‐index for C‐stationary points of a QPCC, that is, for a mathematical program with a quadratic objective function and linear complementarity constraints. The C‐index characterizes the qualitative local behavior of a QPCC around a nondegenerate C‐stationary point. The article focuses on the structure of the C‐stationary set of QPCCs depending on a real parameter. We show that, for generic QPCC data, the C‐index changes exactly at turning points of the C‐stationary set, and that it changes by exactly one. To illustrate this concept, we introduce and analyze two homotopy methods for finding C‐stationary points. Numerical results illustrate that, for randomly generated test problems, the two homotopy methods very often identify B‐stationary points.