On Generalized Minty and Stampacchia Vector Variational-Like Inequalities and Nonsmooth Vector Optimization Problem Involving Higher Order Strong Invexity
Balendu Bhooshan Upadhyay, Priyanka Mishra · Journal of scientific research · 2020
This paper deals with the relations between generalized Minty vector variational-like inequality problems, generalized Stampacchia vector variational-like inequality problems and a class of nonsmooth vector optimization problems by using the concept of an efficient minimizer of order m in terms of Clarke subdifferential.Furthermore, we consider weak formulations of considered generalized Minty and Stampacchia vector variational-like inequality problems and establish the relationship between the solution of these vector variationallike inequality problems and strict minimizer of order m of considered nonsmooth vector optimization problem.Moreover, we employ KKM-Fan theorem to establish some existence results for the solutions of the generalized Minty and Stampacchia vector variational-like inequality problems.The results of the paper extend and unify some earlier results of Bhatia (2008), Li & Yu (2017) and Upadhyay et al. (2017) to the nondifferentiable case as well as for a more general class of nonconvex functions.