General viscosity iterative approximation for solving unconstrained convex optimization problems

摘要

In this paper, we combine a sequence of contractive mappings { h n } ${h_{n}}$ with the proximal operator and propose a generalized viscosity approximation method for solving the unconstrained convex optimization problems in a real Hilbert space H. We show that, under reasonable parameter conditions, our algorithm strongly converges to the unique solution of a variational inequality problem. Our result presented in the paper improves and extends the corresponding results reported by many authors recently.