New Generalized Second-Order Contingent Epiderivatives and Set-Valued Optimization Problems

Some properties of second-order contingent epiderivatives and its applications to vector equilibrium problems

“…Let M be a nonempty subset of Y , a direction u ∈ Y, and a vector z ∈ clM. The following second-order contingent sets will be used in this article (see [1,2,3,5,7,15]). …”

“…( [5,7,8,10,11,12]) We say that y ∈ M is an ideal minimal point (resp. maximal point) of M with respect to Q if a ≥ y (resp.…”

“…They have been used to establish second-order necessary and sufficient efficiency conditions for efficient solution types of vector equilibrium problems with constraints, see, for instance, Li, Zhu and Teo [5]. Basing on the concepts of secondorder contingent sets, the second-order contingent epiderivatives of a single-valued map are E-mail address: suanalysis@gmail.com.…”

“…Basing on the concepts of secondorder contingent sets, the second-order contingent epiderivatives of a single-valued map are E-mail address: suanalysis@gmail.com. established; see [1,2,3,5,6,7] and the references therein. It is known that the existence results of the generalized second-order contingent epiderivative has been studied; see [5] and the references therein.…”

“…It is known that the vector equilibrium problem provides a unified mathematical model including vector complementarity problems, vector saddle point problems, vector optimization problems and vector variational inequality problems as special cases. A large number of results for vector equilibrium problem have been investigated consists of existences of solutions, see, for instance, Marín and Sama [8] and optimality conditions, see, for instance, [1,2,3,4,5,6,7,9,10,11,12,13,14,15,16] and the references therein.…”