Solving Yosida inclusion problem in Hadamard manifold

Abstract

We consider a Yosida inclusion problem in the setting of Hadamard manifolds. We study Korpelevich-type algorithm for computing the approximate solution of Yosida inclusion problem. The resolvent and Yosida approximation operator of a monotone vector field and their properties are used to prove that the sequence generated by the proposed algorithm converges to the solution of Yosida inclusion problem. An application to our problem and algorithm is presented to solve variational inequalities in Hadamard manifolds.

Yosida Approximation Iterative Methods for Split Monotone Variational Inclusion Problems

“…It is well known that set-valued monotone operator can be regularized into a single-valued monotone operator by the process known as the Yosida approximation. Yosida approximation is a tool to solve a variational inclusion problem using nonexpansive resolvent operator and has been used to solve various variational inclusions and system of variational inclusions in linear and nonlinear spaces (see, for example, [18,[25][26][27][28][29][30]). Due to the fact that the zero of Yosida approximation operator associated with monotone operator G is the zero of inclusion problem 0 ∈ GðxÞ and inspired by the work of Moudafi, Byrne, Kazmi, and Dilshad et al, our motive is to propose two iterative methods to solve S p MVIP.…”