Subdifferential and optimality conditions for the difference of set-valued mappings

Subdifferential and optimality conditions for the difference of set-valued mappings In this paper, an existence theorem of the subgradients for set-valued mappings, which introduced by Borwein (Math Scand 48:189–204, 1981), and relations between this subdifferential and the subdifferential introduced by Baier and Jahn (J Optim Theory Appl 100:233–240, 1999), are obtained. By using the concept of this subdifferential, the sufficient optimality conditions for generalized D.C. multiobjective optimization problems are established. And the necessary optimality conditions, which are the generalizations of that in Gadhi (Positivity 9:687–703, 2005), are also established. Moreover, by using a special scalarization function, a real set-valued optimization problem is introduced and the equivalent relations between the solutions are proved for the real set-valued optimization problem and a generalized D.C. multiobjective optimization problem. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

Subdifferential and optimality conditions for the difference of set-valued mappings

Positivity , Volume 16 (2) – Jun 2, 2011

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Publisher
Springer Journals
Copyright
Copyright © 2011 by Springer Basel AG
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Fourier Analysis; Operator Theory; Econometrics; Potential Theory
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-011-0128-6
Publisher site
See Article on Publisher Site

Abstract

In this paper, an existence theorem of the subgradients for set-valued mappings, which introduced by Borwein (Math Scand 48:189–204, 1981), and relations between this subdifferential and the subdifferential introduced by Baier and Jahn (J Optim Theory Appl 100:233–240, 1999), are obtained. By using the concept of this subdifferential, the sufficient optimality conditions for generalized D.C. multiobjective optimization problems are established. And the necessary optimality conditions, which are the generalizations of that in Gadhi (Positivity 9:687–703, 2005), are also established. Moreover, by using a special scalarization function, a real set-valued optimization problem is introduced and the equivalent relations between the solutions are proved for the real set-valued optimization problem and a generalized D.C. multiobjective optimization problem.

Journal

PositivitySpringer Journals

Published: Jun 2, 2011

References

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