On Higher-Order Mixed Duality in Set-Valued Optimization
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Anh, N.L.H.: Higher-order optimality conditions in set-valued optimization using Studniarski derivatives and applications to duality. Positivity 18, 449–473 (2014)
Anh, N.L.H., Khanh, P.Q.: Higher-order optimality conditions in set-valued optimization using radial sets and radial derivatives. J. Glob. Optim. 56, 519–536 (2013)
Anh, N.L.H., Khanh, P.Q.: Higher-order optimality conditions for proper efficiency in nonsmooth vector optimization using radial sets and radial derivatives. J. Glob. Optim. 58, 693–709 (2014)
Anh, N.L.H., Khanh, P.Q., Tung, L.T.: Variational sets: calculus rules and applications to nonsmooth vector optimization. Nonlinear Anal. TMA 74, 2358–2379 (2011)
Aubin, J.P., Frankowska, H.: Set-Valued Analysis. Birkhauser, Boston (1990)
Cambini, R., Carosi, L.: Mixed type duality for multiobjective optimization problems with set constraints. In: Jimenez, M.A., Garzon, G.R., Lizana, A.R. (eds.) Optimality Conditions in Vector Optimization, pp. 119–142. Bentham Science Publishers, Sharjah (2010)
Chen, C.R., Li, S.J., Teo, K.L.: Higher-order weak epiderivatives and applications to duality and optimality conditions. Comput. Math. Appl. 57, 1389–1399 (2009)
Diem, H.T.H., Khanh, P.Q., Tung, L.T.: On higher-order sensitivity analysis in nonsmooth vector optimization. J. Optim. Theory Appl. 162, 463–488 (2014)
Durea, M.: Optimality conditions for weak and firm efficiency in set-valued optimization. J. Math. Anal. Appl. 344, 1018–1028 (2008)
Gong, X.-H., Dong, H.-B., Wang, S.-Y.: Optimality conditions for proper efficient solutions of vector set-valued optimization. J. Math. Anal. Appl. 284, 332–350 (2003)
Li, S.J., Chen, C.R.: Higher-order optimality conditions for Henig efficient solutions in set-valued optimization. J. Math. Anal. Appl. 323, 1184–1200 (2006)
Li, S.J., Meng, K.W., Penot, J.-P.: Calculus rules for derivatives of multimaps. Set Valued Anal. 17, 21–39 (2009)
Li, S.J., Teo, K.L., Yang, X.Q.: Higher-order Mond–Weir duality for set-valued optimization. J. Comput. Appl. Math. 217, 339–349 (2008)
Li, S.J., Teo, K.L., Yang, X.Q.: Higher-order optimality conditions for set-valued optimization. J. Optim. Theory Appl. 137, 533–553 (2008)
Maugeri, A., Puglisi, D.: Non-convex strong duality via subdifferential. Numer. Func. Anal. Optim. 35, 1095–1112 (2014)
Mordukhovich, B.S.: Variational Analysis and Generalized Differentiation, vol. I. Basic Theory. Springer, Berlin (2006)
Mordukhovich, B.S.: Variational Analysis and Generalized Differentiation, vol. II. Applications. Springer, Berlin (2006)
Mordukhovich, B.S.: Generalized differential calculus for nonsmooth and set-valued mappings. J. Math. Anal. Appl. 183, 250–288 (1994)
Rockafellar, R.T., Wets, R.J.B.: Variational Analysis, 3rd edn. Springer, Berlin (2009)
Sach, P.H., Craven, B.D.: Invex multifunctions and duality. Numer. Func. Anal. Optim. 12, 575–591 (1991)
Taa, A.: Set-valued derivatives of multifunctions and optimality conditions. Numer. Func. Anal. Optim. 19, 121–140 (1998)
Tanaka, T., Kuroiwa, D.: The convexity of $$A$$ A and $$B$$ B assures $${\rm int}A + B = {\rm int}(A+B)$$ int A + B = int ( A + B ) . Appl. Math. Lett. 6, 83–86 (1993)