Iterative Algorithms And Its Applications For The Zero Points Problems Of The Monotone Operators In Hilbert Spaces

The zero points problem of monotone operators has given the unite frame of many nonlinear problems, so it has significant value of the scientific research and the practical application. In this paper, two iterative algorithms are proposed for the zero points problem of monotone operators and the constrained convex optimization problems in Hilbert spaces. One is based on the viscosity approximation method and the regularized gradient-projection algorithm, which is for solving the common solution of the zero points problem of monotone operators and the constrained convex optimization problems. In this paper, the author proposes the strong convergence theorem and applies the strong convergence theorem to solve the split feasibility problem and the equilibrium problem. The other regularization algorithm is for solving the common solution of the zero points problem of monotone operators and the fixed point problem and also the generalized equilibrium problem, and then the author obtains the strong convergence theorem and its corollaries for the above problems. The results of this paper extend the corresponding conclusions proposed by many authors.The specific research content of this paper is mostly composed the following two aspects.One is for the zero points problem of the monotone operators and the constrained convex optimization problem in Hilbert spaces, the author proposes an iterative algorithm which is based on the viscosity approximation method and the regularized gradient-projection algorithm, and then proves that this algorithm converges strongly to the common solution of the above two problems.The other is for the zero points problem of the monotone operators and the fixed point problem and also the generalized equilibrium problem in Hilbert spaces, the author constructs a new iterative method for solving the common solution of the above three problems, and then proves the strong convergence of this algorithm under proper conditions.