A generalized hybrid steepest descent method and applications

Abstract

The purpose of this paper is to investigate a generalized hybrid steepest descent method and develop a convergence theory for solving monotone variational inequality over the fixed point set of a mapping which is not necessarily Lipschitz continuous. Using this result, we consider the convex minimization problem for a continuously differentiable convex function whose gradient is not necessarily Lipschitzian. © 2017 Journal of Nonlinear and Variational Analysis