369. Anomalies of the Scholtes regularization for mathematical programs with complementarity constraint
Invited abstract in session MD-7: Methods for simple and nonsmooth bilevel optimization, stream Bilevel and multilevel optimization.
Monday, 16:30-18:30Room: B100/5015
Authors (first author is the speaker)
| 1. | Sebastian Lämmel
|
| Chemnitz University of Technology | |
| 2. | Vladimir Shikhman
|
| Chemnitz University of Technology |
Abstract
For mathematical programs with complementarity constraints (MPCC), we refine the convergence analysis of the Scholtes regularization. Our goal is to relate nondegenerate C-stationary points of MPCC with nondegenerate Karush-Kuhn-Tucker points of its Scholtes regularization. We detected 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.
As a byproduct, we refute a result on the well-posedness of Scholtes regularization wrongly proven in literature.
Keywords
- Global optimization
- Non-smooth optimization
Status: accepted
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