Taiwanese Journal of Mathematics

$\mathbb{T}$-Epiderivatives of Set-valued Maps and Its Application to Set Optimization and Generalized Variational Inequalities

Qamrul Hasan Ansari and Johannes Jahn

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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.

Article information

Taiwanese J. Math., Volume 14, Number 6 (2010), 2447-2468.

First available in Project Euclid: 18 July 2017

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Zentralblatt MATH identifier

Primary: 90C29: Multi-objective and goal programming 49J40: Variational methods including variational inequalities [See also 47J20] 90C26: Nonconvex programming, global optimization 90C48: Programming in abstract spaces

$\mathbb{T}$-cone $\mathbb{T}$-epiderivative contingent epiderivative radial epiderivative $S$-epiderivative optimality conditions vector optimization problem generalized vector $\mathbb{T}$-variational inequality problem existence results


Ansari, Qamrul Hasan; Jahn, Johannes. $\mathbb{T}$-Epiderivatives of Set-valued Maps and Its Application to Set Optimization and Generalized Variational Inequalities. Taiwanese J. Math. 14 (2010), no. 6, 2447--2468. doi:10.11650/twjm/1500406084. https://projecteuclid.org/euclid.twjm/1500406084

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