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

Max Bucher and Alexandra Schwartz ()
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Max Bucher: Technische Universität Darmstadt
Alexandra Schwartz: Technische Universität Darmstadt

Journal of Optimization Theory and Applications, 2018, vol. 178, issue 2, No 4, 383-410

Abstract: 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.

Keywords: Cardinality constraints; Strong stationarity; Mordukhovich stationarity; Second-order optimality conditions; Regularization method; Scholtes regularization; 90C27; 90C30; 90C33; 90C46; 65K05 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-018-1320-7

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