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4159. Extended convergence analysis of the Scholtes-type regularization for cardinality-constrained optimization problems
Invited abstract in session WC-41: Nonsmooth optimization algorithms I, stream Nonsmooth Optimization.
Wednesday, 12:30-14:00Room: 97 (building: 306)
Authors (first author is the speaker)
| 1. | Sebastian Lämmel
|
| Chemnitz University of Technology | |
| 2. | Vladimir Shikhman
|
| Chemnitz University of Technology |
Abstract
We extend the convergence analysis of the Scholtes-type regularization method for cardinality-constrained optimization problems. Its behavior is clarified in the vicinity of saddle points, and not just of minimizers as it has been done in the literature before. This becomes possible by using as an intermediate step the recently introduced regularized continuous reformulation of a cardinality-constrained optimization problem. We show that the Scholtes-type regularization method is well-defined locally
around a nondegenerate T-stationary point of this regularized continuous reformulation. Moreover,
the nondegenerate Karush-Kuhn-Tucker points of the corresponding Scholtes-type regularization converge to a T-stationary point having the same index, i.e. its topological type persists. As consequence, we conclude that the global structure of the Scholtes-type regularization essentially coincides with that of CCOP.
Keywords
- Global Optimization
- Non-smooth Optimization
- Mathematical Programming
Status: accepted
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