Regularization Modification Algorithms And Application Of Solution Of The Minimization Problem

The fixed point problems of nonlinear operators is an important branch of nonlinear disciplines. Fixed point theory is the most important ideas and tools when dealing with nonlinear problems, and plays an important rool in solving constrained convex minimization problems, split feasibility problems and equilibrium problems.In this paper, we use the idea of regularization to establish implicit and explicit iterative methods for finding the approximate minimize of a constrained convex minimization problem in Hilbert space. We also introduce two hybrid methods for finding the common solution of equilibrium problem and constrained convex minimization problem in a real Hilbert space. This paper includes there sections:Chapter 1: we recall the history and present situation of iteration algotithms for solving fixed point problems of nonlinear operators, and we also give a summary of author's work.Chapter 2: we use the idea of regularization to establish implicit and explicit iterative methods for finding the approximate minimizer of a constrained convex minimization problem in a Hilbert space and obtain strong convergence theorems under suitable conditions. It is also used to solve the corresponding variational inequality.Chapter 3: we propose two hybrid methods(one implicit and one explicit) for finding the common solution of equilibrium problem and constrained convex minimization problem in a real Hilbert space and obtain strong convergence theorems under suitable conditions. It is also used to solve the corresponding variational inequality.