New optimality conditions for unconstrained vector equilibrium problem in terms of contingent derivatives in Banach spaces

Duality results for interval-valued pseudoconvex optimization problem with equilibrium constraints with applications

“…In the sequel, we provide the concepts of contingent derivative, epiderivative and hypoderivative, which were first introduced in the books of Aubin and Frankowska and Luc (see Aubin and Frankowska 1990;Luc 1989 for more details), used after by many authors such as Luc (1991), Rodríguez-Marín and Sama (2007a, b), and Su (2016Su ( , 2018; Su and Hien (2019).…”

“…The notion of contingent epiderivatives with pseudoconvex functions was first introduced in the book of Aubin and Frankowska (1990), used after by many other authors, which these is one of the good calculus tools for establishing optimality conditions in vector optimization (see, e.g. Aubin 1981;Aubin and Frankowska 1990;Khan 2003, 2013;Jahn and Rauh 1997;Jiménez and Novo 2008;Jiménez et al 2009;Luc 1989Luc , 1991Luu and Hang 2015;Luu and Su 2018;Rodríguez-Marín and Sama 2007a, b;Su 2016Su , 2018Su and Hien 2019 and the references therein). These notion plays a key role for constructing Mond-Weir and Wolfe dual models for the interval-valued optimization problems with equilibrium constraints, and as well as for establishing weak and strong duality theorems for the same.…”