Optimality conditions and duality for set-valued optimization in terms of cone-directed Clarke derivatives
Abstract
Tóm tắt
Article Details
References
Anh,N.L.H., 2016. Mixed type duality for set-valued optimization problems via higher-order radial epiderivatives. Numerical Functional Analysis and Optimization. 37(7): 823–838.
Arora,R. and Lalitha,C.S., 2005. Proximal proper efficiency in set-valued optimization.Omega -The International Journal of Management Science. 33(5): 407–411.
Aubin,J.P. and Frankowska,H., 1990. Set-Valued Analysis. Birkhäuser, Boston, 461 pages.
Chen,C.R., Li,S.J. and Teo,K.L., 2009. Higher order weak epiderivatives and applications to duality and optimality conditions. Computers & Mathematics with Applications. 57(8): 1389–1399.
Clarke,F.H., 1983. Optimization and nonsmooth analysis.John Wiley, New York, 321 pages.
Corley,H.W., 1988. Optimality conditions for maximizations of set-valued functions. Journal of Optimization Theory and Application. 58(1): 1–10.
Jahn,J., 2009. Vector Optimization. Springer, Berlin, 481 pages.
Jahn,J. and Khan,A.A., 2002. Generalized contingent epiderivative in set-valued optimization: Optimality conditions. Numerical Functional Analysis and Optimization. 23(7–8): 807–831.
Khan,A.A., Tammer,C. and Zănilescu,C., 2016. Set-Valued Opimization. Springer, Berlin, 765 pages.
Lalitha,C.S. and Arora,R., 2008. Weak Clarke epiderivative in set-valued optimization. Journal of Mathematical Analysis and Applications. 342(1): 704–714.
Lalitha C.S. and Arora,R., 2009. Proper Clarke epiderivative in set-valued optimization. Taiwanese Journal of Mathematics. 13(6A): 1695–1710.
Li,S.J, Teo,K.L. and Yang X.Q., 2008. Higher-order Mond–Weir duality for set-valued optimization. Journal of Computational and Applied Mathematics. 217(2): 339–349.
Mond,B. and Weir,T., 1981. Generalized concavity and duality. In: S. Schaible, W.T. Ziemba (Eds.), Generalized Concavity in Optimization and Economics, Academic Press, New York. 263–279.
Sach,P.H. and Craven,B.D., 1991. Invexity in multifunction optimization. Numerical Functional Analysis and Optimization. 12(3–4): 383–394.
Wolfe,P., 1961. A duality theorem for nonlinear programming. Quarterly of Applied Mathematics. 19(3): 239–244.
Tung,L.T., 2017. Strong Karush-Kuhn-Tucker optimality conditions and duality for nonsmooth multiobjective semi-infinite programming via Michel-Penot subdifferential. Journal of Nonlinear Functional Analysis. 2017: 1–21. DOI: 10.23952/jnfa.2017.49
Tung,L.T., Khai,T.T., Hung,P.T. and Ngoc,P.L.B., 2019. Karush-Kuhn-Tucker optimality conditions and duality for set optimization problems with mixed constraints, Journal of Applied and Numerical Optimization. 1(3): 277–291.
Yu,G. and Kong,X., 2016. Optimality and duality in set-valued optimization using higher-order radial derivatives. Statistics, Optimization & Information Computing. 4(2): 154–162.