Nonsmooth pseudo-linear vector optimization and vector variational inequalities on Hadamard manifolds

Abstract

In this paper, we present geodesic pseudo-linear function and pseudo-affine
operator defined on Hadamard manifolds involving Clarke sub-differential and study some characterizations of the function mentioned above. We consider a nonsmooth pseudolinear vector optimization problem and generalized vector variational inequality problems on Hadamard manifolds and establish relationships between solutions to these considered problems. Moreover, a set-valued gap function investigates for a nonsmooth pseudo-linear vector optimization problem. A numerical example is constructed to evaluate the result of this paper.