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On calmness of the argmin mapping in parametric optimization problems


Klatte, Diethard; Kummer, Bernd (2015). On calmness of the argmin mapping in parametric optimization problems. Journal of Optimization Theory and Applications, 165(3):708-719.

Abstract

Recently, Cánovas et al. presented an interesting result: the argmin mapping of a linear semi-infinite program under canonical perturbations is calm if and only if some associated linear semi-infinite inequality system is calm. Using classical tools from parametric optimization, we show that the if-direction of this condition holds in a much more general framework of optimization models, while the opposite direction may fail in the general case. In applications to special classes of problems, we apply a more recent result on the intersection of calm multifunctions.

Abstract

Recently, Cánovas et al. presented an interesting result: the argmin mapping of a linear semi-infinite program under canonical perturbations is calm if and only if some associated linear semi-infinite inequality system is calm. Using classical tools from parametric optimization, we show that the if-direction of this condition holds in a much more general framework of optimization models, while the opposite direction may fail in the general case. In applications to special classes of problems, we apply a more recent result on the intersection of calm multifunctions.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:03 Faculty of Economics > Department of Business Administration
Dewey Decimal Classification:330 Economics
Language:English
Date:2015
Deposited On:24 Oct 2014 16:03
Last Modified:08 Sep 2017 03:55
Publisher:Springer
ISSN:1573-2878
Publisher DOI:https://doi.org/10.1007/s10957-014-0643-2
Other Identification Number:merlin-id:10435

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