Jahn J, Ansari Q (2010)
Publication Type: Journal article, Original article
Publication year: 2010
Book Volume: 14
Pages Range: 2447-2468
In this paper, we first define a 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 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 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 T-variational inequality problem are given.
APA:
Jahn, J., & Ansari, Q. (2010). T-epiderivatives of set-valued maps and its application to set optimization and generalized variational inequalities. Taiwanese Journal of Mathematics, 14, 2447-2468.
MLA:
Jahn, Johannes, and Q.H. Ansari. "T-epiderivatives of set-valued maps and its application to set optimization and generalized variational inequalities." Taiwanese Journal of Mathematics 14 (2010): 2447-2468.
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