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Extremality, Stationarity and Generalized Separation of Collections of Sets

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Open access
Authors
Bui, Hoa
Kruger, A.Y.
Date
2019
Type
Journal Article

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Bui, H.T. and Kruger, A.Y. 2019. Extremality, Stationarity and Generalized Separation of Collections of Sets. Journal of Optimization Theory and Applications. 182 (1): pp. 211-264.
Source Title
Journal of Optimization Theory and Applications
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Faculty
Faculty of Science and Engineering
School
School of Electrical Engineering, Computing and Mathematical Sciences (EECMS)
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This is a post-peer-review, pre-copyedit version of an article published in Journal of Optimization Theory and Applications. The final authenticated version is available online at: http://doi.org/10.1007/s10957-018-01458-8.

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Abstract

© 2018, Springer Science+Business Media, LLC, part of Springer Nature. The core arguments used in various proofs of the extremal principle and its extensions as well as in primal and dual characterizations of approximate stationarity and transversality of collections of sets are exposed, analysed and refined, leading to a unifying theory, encompassing all existing approaches to obtaining ‘extremal’ statements. For that, we examine and clarify quantitative relationships between the parameters involved in the respective definitions and statements. Some new characterizations of extremality properties are obtained.