Regularization Inertial Proximal Point Algorithm for Monotone Hemicontinuous Mapping and Inverse Strongly Monotone Mappings in Hilbert Spaces

Regularization Inertial Proximal Point Algorithm for Monotone Hemicontinuous Mapping and Inverse Strongly Monotone Mappings in Hilbert Spaces

An Extragradient Method and Proximal Point Algorithm for Inverse Strongly Monotone Operators and Maximal Monotone Operators in Banach Spaces

We introduce an iterative scheme for finding a common element of the solution set of a maximal monotone operator and the solution set of the variational inequality problem for an inverse strongly-monotone operator in a uniformly smooth and uniformly convex Banach space, and then we prove weak and strong convergence theorems by using the notion of generalized projection. The result presented in ...

Convergence Theorems for Nonexpansive Mappings and Inverse-strongly Monotone Mappings

In this paper, we introduce a general iterative scheme for finding a common element of the set of common fixed points of an infinite family of nonexpansive mappings and the set of solutions of variational inequalities for an inverse-strongly monotone mapping.

Convergence Theorems of Approximate Proximal Point Algorithm for Zeroes of Maximal Monotone Operators in Hilbert Spaces

In this paper, we introduce two kinds of iterative algorithms for finding zeroes of maximal monotone operators, and establish strong and weak convergence theorems of the modified proximal point algorithms. By virtue of the established theorems, we consider the problem of finding a minimizer of a convex function. Mathematics Subject Classification: Primary 47H17; Secondary 47H05, 47H10

Convergence of a proximal point algorithm for maximal monotone operators in Hilbert spaces

* Correspondence: hbshigh@yeah. net College of Science, Hebei University of Engineering, Handan 056038, China Full list of author information is available at the end of the article Abstract In this article, we consider the proximal point algorithm for the problem of approximating zeros of maximal monotone mappings. Strong convergence theorems for zero points of maximal monotone mappings are est...