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Applicant:
Indian Institute of Technology (IIT) Patna 
Author:
B B Upadhyay; P Mishra 
Corresponding Authors:
Priyanka Mishra 
DOI #:
http://dx.doi.org/10.37398/JSR.2020.640139 
Title:
On generalized Minty and Stampacchia vector variational like inequalities and nonsmooth vector optimization problem involving higher order strong convexity, 
Journal:
Journal of Scientific Research 
Year:
2020 
Volume:
64(1) 
Page:
182-191 
Keywords:
Efficient minimizers of order m, KKM-Fan theorem, locally Lipschitz functions, strict minimizers of order m, vector variational-like inequality problems. 
Abstract:
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 
Entered by:
Venkata Dantham on 2020-08-04 
 
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