Michael Reichel (ari)
Es spricht Prof. Dr. Vladimir Shikhman (TU Chemnitz)
zum Thema: Anomalies of the Scholtes regularization for mathematical programs with complementarity constraints
Abstract:
We discuss the difficulties and challenges if solving mathematical programs with complementarity constraints (MPCC) by means of regularization methods. Before refining the convergence analysis of the Scholtes regularization, we briefly explain the critical point theory for MPPCs in terms understandable for the general mathematical audience. Our goal will be then to relate nondegenerate C-stationary points of MPCC with nondegenerate Karush-Kuhn-Tucker points of its Scholtes regularization. By doing so, we present the following anomalies: (i) in a neighborhood of a nondegenerate C-stationary point there could be degenerate Karush-Kuhn-Tucker points of the Scholtes regularization; (ii) even if nondegenerate, they might be locally non-unique; (iii) if nevertheless unique, their quadratic index potentially differs from the C-index of the C-stationary point under consideration. Thus, a change of the topological type for Karush-Kuhn-Tucker points of the Scholtes regularization is possible. In particular, a nondegenerate minimizer of MPCC might be approximated by saddle points. In order to bypass the mentioned anomalies, an additional generic condition for nondegenerate C-stationary points of MPCC is identified. Then, we uniquely trace nondegenerate Karush-Kuhn-Tucker points of the Scholtes regularization and successively maintain their topological type. In collaboration with Sebastian Lämmel.
Dienstag, 8. Juli 2025, 15:00 Uhr, Curie Hörsaal
(Kaffee ab 14:30 Uhr im Raum C 325)
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