Header

UZH-Logo

Maintenance Infos

Optimization methods and stability of inclusions in Banach Spaces


Klatte, Diethard; Kummer, Bernd (2009). Optimization methods and stability of inclusions in Banach Spaces. Mathematical Programming, 117(1-2):305-330.

Abstract

Our paper deals with the interrelation of optimization methods and Lipschitz stability of multifunctions in arbitrary Banach spaces. Roughly speaking, we show that linear convergence of several first order methods and Lipschitz stability mean the same. Particularly, we characterize calmness and the Aubin property by uniformly (with respect to certain starting points) linear convergence of descent methods and approximate projection methods. So we obtain, e.g., solution methods (for solving equations or variational problems) which require calmness only. The relations of these methods to several known basic algorithms are discussed, and errors in the subroutines as well as deformations of the given mappings are permitted. We also recall how such deformations are related to standard algorithms like barrier, penalty or regularization methods in optimization.

Abstract

Our paper deals with the interrelation of optimization methods and Lipschitz stability of multifunctions in arbitrary Banach spaces. Roughly speaking, we show that linear convergence of several first order methods and Lipschitz stability mean the same. Particularly, we characterize calmness and the Aubin property by uniformly (with respect to certain starting points) linear convergence of descent methods and approximate projection methods. So we obtain, e.g., solution methods (for solving equations or variational problems) which require calmness only. The relations of these methods to several known basic algorithms are discussed, and errors in the subroutines as well as deformations of the given mappings are permitted. We also recall how such deformations are related to standard algorithms like barrier, penalty or regularization methods in optimization.

Statistics

Citations

Dimensions.ai Metrics
36 citations in Web of Science®
37 citations in Scopus®
Google Scholar™

Altmetrics

Downloads

40 downloads since deposited on 28 Aug 2019
10 downloads since 12 months
Detailed statistics

Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:03 Faculty of Economics > Department of Business Administration
Dewey Decimal Classification:330 Economics
Scopus Subject Areas:Physical Sciences > Software
Physical Sciences > General Mathematics
Scope:Discipline-based scholarship (basic research)
Language:English
Date:March 2009
Deposited On:28 Aug 2019 15:17
Last Modified:21 Jun 2024 02:07
Publisher:Springer
ISSN:0025-5610
Additional Information:The original publication is available at www.springerlink.com. It was published electronically in 2007.
OA Status:Green
Publisher DOI:https://doi.org/10.1007/s10107-007-0174-9
Related URLs:http://search.ebscohost.com/login.aspx?direct=true&db=buh&AN=32960991&loginpage=Login.asp&site=ehost-live
Other Identification Number:merlin-id:885
  • Content: Published Version