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

• 成果类型: Article
• 署名作者: Ralph, Daniel; Stein, Oliver
• 署名单位: University of Cambridge; Helmholtz Association; Karlsruhe Institute of Technology
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.1110.0501
• 发表日期: 2011
• 页码: 504-526
• 关键词: mathematical programs; elastic-mode; CONVERGENCE; point; Penalization; regularization; stationarity; algorithms; scheme

摘要

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.