Abstract
In this paper, we first define a $\mathbb{T}$-cone which is a unified version of several cones, namely, contingent cone, radial cone, $C$-tangent cone, Clarke tangent cone, $S$-cone, adjacent cone, etc. Then, we define the $\mathbb{T}$-epiderivative of a set-valued map which includes the contingent epiderivative, radial epiderivative, $S$-epiderivative, adjacent epiderivative etc. as special cases. We present several properties of such an epiderivative. The generalized vector $\mathbb{T}$-variational inequality problem is also considered. We provide necessary and sufficient conditions for a solution of a set optimization problem. Several existence results for solutions of set optimization problems and a generalized vector $\mathbb{T}$-variational inequality problem are given.
Citation
Qamrul Hasan Ansari. Johannes Jahn. "$\mathbb{T}$-Epiderivatives of Set-valued Maps and Its Application to Set Optimization and Generalized Variational Inequalities." Taiwanese J. Math. 14 (6) 2447 - 2468, 2010. https://doi.org/10.11650/twjm/1500406084
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