Weak Subdifferential of Set-Valued Mappings
In this note we introduce a notion of the weak contingent generalized gradient for set-valued mappings associated with the contingent epiderivative of set-valued mappings introduced in "E. Bednarczuk and W. Song (1998). Contingent epiderivative and its applications to set-valued optimization. C...
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| Published in | Optimization Vol. 52; no. 3; pp. 263 - 276 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Taylor & Francis Group
01.06.2003
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0233-1934 1029-4945 |
| DOI | 10.1080/0233193031000120051 |
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| Abstract | In this note we introduce a notion of the weak contingent generalized gradient for set-valued mappings associated with the contingent epiderivative of set-valued mappings introduced in "E. Bednarczuk and W. Song (1998). Contingent epiderivative and its applications to set-valued optimization. Control and Cybernetics, 27, 376-386; G.Y. Chen and J. Jahn (1998). Optimally conditions for set-valued optimization problems. Mathematical Methods of Operations Research, 48, 187-200." and prove that, under some additional condition, it coincides with the weak subdifferential introduced in "T. Tanino (1992). Conjugate duality in vector optimization. Journal of Mathematical Analysis and Applications, 167, 84-97." when the set-valued map is cone-convex. We also study the weak contingent generalized gradient of a sum of two set-valued mappings and optimality conditions for a set-valued vector optimization problem. |
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| AbstractList | In this note we introduce a notion of the weak contingent generalized gradient for set-valued mappings associated with the contingent epiderivative of set-valued mappings introduced in "E. Bednarczuk and W. Song (1998). Contingent epiderivative and its applications to set-valued optimization. Control and Cybernetics, 27, 376-386; G.Y. Chen and J. Jahn (1998). Optimally conditions for set-valued optimization problems. Mathematical Methods of Operations Research, 48, 187-200." and prove that, under some additional condition, it coincides with the weak subdifferential introduced in "T. Tanino (1992). Conjugate duality in vector optimization. Journal of Mathematical Analysis and Applications, 167, 84-97." when the set-valued map is cone-convex. We also study the weak contingent generalized gradient of a sum of two set-valued mappings and optimality conditions for a set-valued vector optimization problem. |
| Author | Song, Wen |
| Author_xml | – sequence: 1 givenname: Wen surname: Song fullname: Song, Wen organization: Department of Mathematics , Harbin Normal University |
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| Copyright | Copyright Taylor & Francis Group, LLC 2003 |
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| StartPage | 263 |
| SubjectTerms | Contingent Epiderivative Mathematics Subject Classification 2000: 49k27 Optimality Conditions Vector Optimization Weak Subdifferentials |
| Title | Weak Subdifferential of Set-Valued Mappings |
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