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Journal of Inequalities and Applications

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Open Access 01.12.2009 | Research Article

Higher-Order Weakly Generalized Adjacent Epiderivatives and Applications to Duality of Set-Valued Optimization

verfasst von: Q. L. Wang, S. J. Li

Erschienen in: Journal of Inequalities and Applications | Ausgabe 1/2009

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Abstract

A new notion of higher-order weakly generalized adjacent epiderivative for a set-valued map is introduced. By virtue of the epiderivative and weak minimality, a higher-order Mond-Weir type dual problem and a higher-order Wolfe type dual problem are introduced for a constrained set-valued optimization problem, respectively. Then, corresponding weak duality, strong duality, and converse duality theorems are established.

Vorheriger Artikel A New Singular Impulsive Delay Differential Inequality and Its Application

Nächster Artikel On Solvability of a Generalized Nonlinear Variational-Like Inequality

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Jahn J, Rauh R: Contingent epiderivatives and set-valued optimization. Mathematical Methods of Operations Research 1997,46(2):193–211. 10.1007/BF01217690MATHMathSciNetCrossRef

Chen GY, Jahn J: Optimality conditions for set-valued optimization problems. Mathematical Methods of Operations Research 1998,48(2):187–200. 10.1007/s001860050021MATHMathSciNetCrossRef

Lalitha CS, Arora R: Weak Clarke epiderivative in set-valued optimization. Journal of Mathematical Analysis and Applications 2008,342(1):704–714. 10.1016/j.jmaa.2007.11.057MATHMathSciNetCrossRef

Aubin J-P, Frankowska H: Set-Valued Analysis, Systems & Control: Foundations & Applications. Volume 2. Birkhäuser, Boston, Mass, USA; 1990:xx+461.MATH

Sach PH, Craven BD: Invex multifunctions and duality. Numerical Functional Analysis and Optimization 1991,12(5–6):575–591. 10.1080/01630569108816453MATHMathSciNetCrossRef

Aubin J-P, Ekeland I: Applied Nonlinear Analysis, Pure and Applied Mathematics. John Wiley & Sons, New York, NY, USA; 1984:xi+518.MATH

Sach PH, Yen ND, Craven BD: Generalized invexity and duality theories with multifunctions. Numerical Functional Analysis and Optimization 1994,15(1–2):131–153. 10.1080/01630569408816555MATHMathSciNetCrossRef

Aubin J-P: Contingent derivatives of set-valued maps and existence of solutions to nonlinear inclusions and differential inclusions. In Mathematical Analysis and Applications, Part A, Advances in Mathematics. Supplementary Studies. Volume 7. Edited by: Nachbin L. Academic Press, New York, NY, USA; 1981:159–229.

Penot J-P: Differentiability of relations and differential stability of perturbed optimization problems. SIAM Journal on Control and Optimization 1984,22(4):529–551. 10.1137/0322033MATHMathSciNetCrossRef

10.

Ioffe AD: Calculus of dini subdifferentials of functions and contingent coderivatives of set-valued maps. Nonlinear Analysis: Theory, Methods & Applications 1984,8(5):517–539. 10.1016/0362-546X(84)90091-9MATHMathSciNetCrossRef

11.

Liu Z-B, Kim JK, Huang N-J: Existence of solutions for nonconvex and nonsmooth vector optimization problems. Journal of Inequalities and Applications 2008, 2008:-7.

12.

Shi DS: Contingent derivative of the perturbation map in multiobjective optimization. Journal of Optimization Theory and Applications 1991,70(2):385–396. 10.1007/BF00940634MATHMathSciNetCrossRef

13.

Yang XQ: Directional derivatives for set-valued mappings and applications. Mathematical Methods of Operations Research 1998,48(2):273–285. 10.1007/s001860050028MATHMathSciNetCrossRef

14.

Gong X-H, Dong H-B, Wang S-Y: Optimality conditions for proper efficient solutions of vector set-valued optimization. Journal of Mathematical Analysis and Applications 2003,284(1):332–350. 10.1016/S0022-247X(03)00360-3MATHMathSciNetCrossRef

15.

Taa A: Set-valued derivatives of multifunctions and optimality conditions. Numerical Functional Analysis and Optimization 1998,19(1–2):121–140. 10.1080/01630569808816819MATHMathSciNetCrossRef

16.

Jiménez B, Novo V: Second order necessary conditions in set constrained differentiable vector optimization. Mathematical Methods of Operations Research 2003,58(2):299–317. 10.1007/s001860300283MATHMathSciNetCrossRef

17.

Jahn J, Khan AA, Zeilinger P: Second-order optimality conditions in set optimization. Journal of Optimization Theory and Applications 2005,125(2):331–347. 10.1007/s10957-004-1841-0MATHMathSciNetCrossRef

18.

Li SJ, Teo KL, Yang XQ: Higher-order optimality conditions for set-valued optimization. Journal of Optimization Theory and Applications 2008,137(3):533–553. 10.1007/s10957-007-9345-3MATHMathSciNetCrossRef

19.

Li SJ, Teo KL, Yang XQ: Higher-order Mond-Weir duality for set-valued optimization. Journal of Computational and Applied Mathematics 2008,217(2):339–349. 10.1016/j.cam.2007.02.011MATHMathSciNetCrossRef

20.

Li SJ, Chen CR: Higher order optimality conditions for Henig efficient solutions in set-valued optimization. Journal of Mathematical Analysis and Applications 2006,323(2):1184–1200. 10.1016/j.jmaa.2005.11.035MATHMathSciNetCrossRef

21.

Luc DT: Theory of Vector Optimization, Lecture Notes in Economics and Mathematical Systems. Volume 319. Springer, Berlin, Germany; 1989:viii+173.

Titel: Higher-Order Weakly Generalized Adjacent Epiderivatives and Applications to Duality of Set-Valued Optimization
verfasst von: Q. L. Wang
S. J. Li
Publikationsdatum: 01.12.2009
Verlag: Springer International Publishing
Erschienen in: Journal of Inequalities and Applications / Ausgabe 1/2009
Elektronische ISSN: 1029-242X
DOI: https://doi.org/10.1155/2009/462637

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