Calculus of directional subdifferentials and coderivatives in Banach spaces

Positivity - Tập 21 - Trang 223-254 - 2016
Pujun Long1, Bingwu Wang2, Xinmin Yang3
1School of Mathematical Sciences, Inner Mongolia University, Hohhot, People’s Republic of China
2Department of Mathematics, Eastern Michigan University, Ypsilanti, USA
3College of Mathematical Sciences, Chongqing Normal University, Chongqing, People’s Republic of China

Tóm tắt

In this work we study the directional versions of Mordukhovich normal cones to nonsmooth sets, coderivatives of set-valued mappings, and subdifferentials of extended-real-valued functions in the framework of general Banach spaces. We establish some characterizations and basic properties of these constructions, and then develop calculus including sum rules and chain rules involving smooth functions. As an application, we also explore the upper estimates of the directional Mordukhovich subdifferentials and singular subdifferentials of marginal functions.

Tài liệu tham khảo

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