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Second-Order Optimality Conditions and Improved Convergence Results for Regularization Methods for Cardinality-Constrained Optimization Problems

Bucher, Max and Schwartz, Alexandra (2018):
Second-Order Optimality Conditions and Improved Convergence Results for Regularization Methods for Cardinality-Constrained Optimization Problems.
In: Journal of Optimization Theory and Applications, pp. 383-410, 178, (2), ISSN 1573-2878, DOI: 10.1007/s10957-018-1320-7, [Online-Edition: https://doi.org/10.1007/s10957-018-1320-7],
[Article]

Abstract

We consider nonlinear optimization problems with cardinality constraints. Based on a continuous reformulation, we introduce second-order necessary and sufficient optimality conditions. Under such a second-order condition, we can guarantee local uniqueness of Mordukhovich stationary points. Finally, we use this observation to provide extended local convergence theory for a Scholtes-type regularization method, which guarantees the existence and convergence of iterates under suitable assumptions. This convergence theory can also be applied to other regularization schemes.

Item Type: Article
Erschienen: 2018
Creators: Bucher, Max and Schwartz, Alexandra
Title: Second-Order Optimality Conditions and Improved Convergence Results for Regularization Methods for Cardinality-Constrained Optimization Problems
Language: English
Abstract:

We consider nonlinear optimization problems with cardinality constraints. Based on a continuous reformulation, we introduce second-order necessary and sufficient optimality conditions. Under such a second-order condition, we can guarantee local uniqueness of Mordukhovich stationary points. Finally, we use this observation to provide extended local convergence theory for a Scholtes-type regularization method, which guarantees the existence and convergence of iterates under suitable assumptions. This convergence theory can also be applied to other regularization schemes.

Journal or Publication Title: Journal of Optimization Theory and Applications
Volume: 178
Number: 2
Uncontrolled Keywords: Mathematics - Optimization and Control (math.OC)
Divisions: Exzellenzinitiative
Exzellenzinitiative > Graduate Schools
Exzellenzinitiative > Graduate Schools > Graduate School of Computational Engineering (CE)
04 Department of Mathematics
04 Department of Mathematics > Optimization
Date Deposited: 11 Sep 2017 12:51
DOI: 10.1007/s10957-018-1320-7
Official URL: https://doi.org/10.1007/s10957-018-1320-7
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