Research Projects

In this project, PI consider the classes of mixed vector quasi-hemivariational inequality problems on Hadamard manifolds and derive the conditions under which the solutions of the considered problems exist. The existence of the solution sets of the considered problems will be established under suitable monotonicity as well as without monotonicity assumptions. Moreover, we shall formulate the gap functions, regularized gap functions and D-gap functions for the considered problems and find the global error bounds. The output of the project could be used to find the iterative algorithms for the considered problems with faster convergence. Moreover, gap functions could be utilized to convert the considered generalized vector variational inequality problems into corresponding vector optimization problems, which will allow the application of powerful optimization techniques to find the solution of considered mixed vector quasi-hemivariational inequality problems. In view of the fact that a nonconvex and nonsmooth optimization problem could be transformed into a convex and smooth ones by choosing a suitable Riemannian metric, the output of the project is applicable to a wider class of vector optimization and vector variational inequality problems.