References
- Bao TQ , Mordukhovich BS . Set-valued optimization in welfare economics. Vol. 13, Advances in mathematical economics. Tokyo: Springer; 2010. p. 113–153.
- Jahn J . Vector optimization -- theory, applications and extensions. Heidelberg: Springer; 2011.
- Neukel N . Order relations of sets and its application in socio-economics. Appl Math Sci. (Ruse) 7. 2013;113--113:5711–5739.
- Luc DT . Theory of vector optimization. Vol. 319, Lecture notes in economics and mathematical systems. Berlin: Springer-Verlag; 1989.
- Kuroiwa D . Natural criteria of set-valued optimization, manuscript. Japan: Shimane University; 1998.
- Hernández E . A survey of set optimization problems with set solutions. Set optimization and applications -- the state of the art. Vol. 151, Springer proceedings in mathematics & statistics. Heidelberg: Springer; 2015. p. 143–158
- Jahn J , Ha TXD . New order relations in set optimization. J Optim Theory Appl. 2011;148:209–236.
- Jahn J . Directional derivative in set optimization with the less oder relation. Taiwanese J Math. 2015;19(3):737–757.
- Aubin J-P , Frankowska H . Set-valued analysis. systems & Control: foundations & applications. Vol. 2. Boston (MA): Birkhäuser Boston Inc; 1990.
- Mordukhovich BS . Variational analysis and generalized differentiation, I: basic theory. Vol. 330, Grundlehren series (Fundamental principles of mathematical sciences). Berlin: Springer; 2006.
- Baier R , Farkhi E . Regularity of set-valued maps and their selections through set differences: part 1: Lipschitz continuity. Serdica Math J. 2013;39:365–390.
- Kuroiwa D . On derivatives and convexity of set-valued maps and optimality conditions in set optimization. J Nonlinear Convex Anal. 2009;10:41–50.
- Hoheisel T , Kanzow C , Mordukhovich BS , Phan H . Generalized Newton’s method based on graphical derivatives. Nonlinear Anal. 2012;75:1324–1340.
- Hamel A , Schrage C . Directional derivatives, subdifferentials and optimality conditions for set-valued convex functions. Pac J Optim. 2014;10(4):667–689.
- Pilecka M . Optimality conditions in set-valued programming using the set criterion, Preprint 2014–02. Germany: Technical University of Freiberg; 2014.
- Crespi GP , Schrage C . Set optimization meets variational inequalities. Set optimization and applications -- the state of the art. Vol. 151, Springer proceedings in mathematics & statistics. Heidelberg: Springer; 2015. p. 213–-247
- Hamel A , Schrage C . Notes on extended real- and set-valued functions. J Convex Anal. 2012;19(2):355–384.
- Demyanov VF , Rubinov AM . Foundations of nonsmooth analysis and quasidifferential calculus. Moscow: Nauka; 1990. Russian.
- Rubinov AM , Akhundov IS . Difference of compact sets in the sense of Demyanov and its application to non-smooth analysis. Optimization. 1992;23:179–188.
- Dempe S , Pilecka M . Optimality conditions for set-valued optimization problems using a modified Demyanov difference. J Optim Theory Appl. 2016;171(2):402–421.
- Ha TXD . Existence and density results for proper efficiency in cone compact sets. J Optim Theory Appl. 2001;111(1):173–194.
- Aubin J-P , Ekeland I . Applied nonlinear analysis. Pure and applied mathematics (New York). A Wiley-Interscience Publication. New York (NY): Wiley; 1984.
- Hiriart-Urruty JB . New concepts in nondifferentiable programming. Bull Soc Math France. 1979;60:57–85.
- Zaffaroni A . Degrees of efficiency and degrees of minimality. SIAM J Control Optim. 2003;42(3):1071–1086.
- Anh Tuan V , Tammer C , Zalinescu C . The Lipschitzianity of convex vector and set-valued functions. TOP. 2016;24(1):273–299.
- Kuroiwa D . Convexity for set-valued maps. Appl Math Lett. 1996;9(2):97–101.
- Kuroiwa D , Tanaka T , Ha TXD . On cone convexity of set-valued maps. Proceedings of the Second World Congress of Nonlinear Analysts, Part 3 (Athens, 1996). Nonlinear Anal. 1997;30(3):1487–1496.
- Zalinescu C . Weak sharp minima, well behaving functions and global error bounds for convex inequalities in Banach spaces. In: Bulatov V , Baturin V , editors. Optimization methods and their applications. Irkutsk: Baikal; 2001. p. 272–284.
- Ha TXD . Estimates of error bounds for some sets of efficient solutions of a set-valued optimization problem. Set optimization and applications -- the state of the art. Vol. 151, Springer proceedings in mathematics & statistics. Heidelberg: Springer; 2015. p. 249–273.
- Ha TXD . Lagrange multipliers for set-valued optimization problems associated with coderivatives. J Math Anal Appl. 2005;311(2):647–663.
- Hiriart-Urruty JB , Lemaréchal C . Convex analysis and minimization algorithms I. New York (NY): Springer; 1993.