Weak Subdifferentials for Set-Valued Mappings

The purpose of this paper is to study the weak subdifferential for set-valued mappings, which was introduced by Chen and Jahn (Math. Methods Oper. Res., 48:187–200, 1998 ). Two existence theorems of weak subgradients for set-valued mappings are obtained. Moreover, some properties of the weak subdiff...

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Bibliographic Details
Published in:Journal of optimization theory and applications 2014-07, Vol.162 (1), p.1-12
Main Authors: Long, X. J., Peng, J. W., Li, X. B.
Format: Article
Language:English
Subjects:
Analysis
Applications of Mathematics
Calculus of Variations and Optimal Control
Optimization
Engineering
Existence theorems
Mapping
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Studies
Theorems
Theory of Computation
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Summary:The purpose of this paper is to study the weak subdifferential for set-valued mappings, which was introduced by Chen and Jahn (Math. Methods Oper. Res., 48:187–200, 1998 ). Two existence theorems of weak subgradients for set-valued mappings are obtained. Moreover, some properties of the weak subdifferential for set-valued mappings are derived. Our results improve the corresponding ones in the literature. Some examples are given to illustrate our results.
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-013-0469-3