Nonsmooth quasi-variational-like inequalities with applications to nonsmooth vector quasi-optimization
Affiliation:
1. King Fahd University of Petroleum & Minerals, Department of Mathematics and Statistics, Dhahran, Saudi Arabia
Abstract
We consider nonsmooth vector quasi-variational-like inequalities and
nonsmooth vector quasioptimization problems. We utilize the method of
scalarization to define nonsmooth quasi-variational-like inequalities by
means of Clarke generalized directional derivative. We then study their
relations with the problem of vector quasi-optimization and its scalarized
version. Under the assumption of pseudomonotonicity and then densely
pseudomonotonicity, we present some existence results for solutions to
nonsmooth quasi-variational-like inequalities. To the best of our knowledge,
the results we obtained are new in the sense of utilizing the scalarization
method.
Publisher
National Library of Serbia
Subject
General Mathematics