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Abstrakty
The set criterion is an appropriate defining approach regarding the solutions for the set-valued optimization problems. By using approximations as generalized derivatives of set-valued mappings, we establish necessary optimality conditions for a constrained set-valued optimization problem in the sense of set optimization in terms of asymptotical pointwise compact approximations. Sufficient optimality conditions are then obtained through first-order strong approximations of data set-valued mappings.
Czasopismo
Rocznik
Tom
Strony
425--444
Opis fizyczny
Bibliogr. 19 poz.
Twórcy
autor
- LAMA, Sidi Mohamed Ben Abdellah University, Dhar El Mahraz, Department of Mathematics, Fes, Morocco
autor
- LAMA, Sidi Mohamed Ben Abdellah University, Dhar El Mahraz, Department of Mathematics, Fes, Morocco
Bibliografia
- Allali, K. and Amahroq, T. (1997) Second order approximations and primal and dual necessary optimality conditions. Optimization 3, 229-246.
- Alonso, M. and Rodríguez-Marín, L. (2008) Optimality conditions for a non convex set-valued optimization problem. Comput. Math. Appl. 56, 82-89.
- Amahroq, T. and Oussarhan, A. (2019) Lagrange multiplier rules for weakly minimal solutions of compact-valued set optimization problems. Asia-Pacific Journal of Operational Research 36, 1-22.
- Aubin, J.-P. and Cellina, A. (1984) Differential Inclusions. Set-Valued Maps and Viability Theory. Grundlehren der Mathematischen Wissenschaften 264, Springer-Verlag, Berlin.
- Jahn, J. (2004) Vector Optimization. Theory, Applications, and Extensions. Springer, Berlin.
- Khanh, P.Q. and Tuan, N.D. (2011) Optimality conditions without continuity in multivalued optimization using approximations as generalized derivatives. In: S.K. Mishra, ed., Recent Contributions in Nonconvex Optimization, 47-61. Springer, New York.
- Khanh, P.Q., Tuan, N.D. (2015) First and second-order optimality conditions without differentiability in multivalued vector optimization. Positivity 19, 817-841.
- Khan, A.A., Tammer, C., Zălinescu, C. (2015) Set-valued Optimization. An Introduction with Applications. Springer, Berlin.
- Klein, E., Thompson, A.C. (1984) Theory of Correspondences. Including Applications to Mathematical Economics. Canadian Mathematical Society Series of Monographs and Advanced Texts, New York.
- Kuroiwa, D. (2008) On Derivatives of Set-Valued Maps in Set Optimization. Manuscript, Shimane University, Japan.
- Kuroiwa, D. (1988) Natural criteria of set-valued optimization. Manuscript, Shimane University, Japan.
- Kuroiwa, D. (2009) On derivatives of set-valued maps and optimality conditions for set optimization. Journal of Nonlinear and Convex Analysis 10, 41-50.
- Kuroiwa, D., Tanaka, T. and Ha, T. X. D. (1997) On cone convexity of set-valued maps. Nonlinear Analysis 30, 1487-1496.
- Luc, D.T. (1989) Theory of Vector Optimization. Lecture Notes in Economics and Mathematical Systems, Theory of Vector Optimization 319, Springer-Verlag, Berlin.
- Mordukhovich, B.S. (2006) Variational Analysis and Generalized Differentiation, II: Applications. Springer, Berlin.
- Rodríguez-Marín, L. and Sama, M. (2007) (Λ,C)-contingent derivatives of set-valued maps. Journal of Mathematical Analysis and Applications 335, 974-989.
- Rodríguez-Marín, L. and Hernández, E. (2007) Nonconvex scalarization in set optimization with set-valued maps. Journal of Mathematical Analysis and Applications 325, 1-18.
- Shi, D.S. (1991) Contingent derivative of perturbed map in multiobjective optimization. Journal of Optimization Theory and Applications 70, 385-395.
- Tanino, T. (1998) Sensitivity analysis in multiobjective optimization. Journal of Optimization Theory and Applications 56, 479-499.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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