Regularization inertial proximal point algorithm for common solutions of a finite family of inverse-strongly monotone equations

The aim of the paper is to propose an iterative regularization method of proximal point type for finding a common solution for a finite family of inverse-strongly monotone equations in Hilbert spaces.     

Convergence rates and finite-dimensional approximation for a class of ill-posed variational inequalities

The purpose of this paper is to investigate an operator version of Tikhonov regularization for a class of ill-posed variational inequalities under arbitrary perturbation operators. Aspects of convergence rate and finite-dimensional approximations are considered. An example in the theory of generalized eigenvectors is given for illustration. Institute of Information Technology, Vietnam. Published in Ukrainskii Matematicheskii Zhunal, Vol. 49, No. 5, pp. 629–637, May, 1997.     

Tikhonov regularization for a general nonlinear constrained optimization problem

The goal of this study is to analyze the Tikhonov regularization method as applied to a general nonlinear optimization problem that has been previously reduced to an unconstrained optimization problem. The stability properties of the method are examined, and its convergence is proved. The text was submitted by the author in English.     

Strong Convergence to Solutions for a Class of Variational Inequalities in Banach Spaces by Implicit Iteration Methods

In this paper, in order to solve a variational inequality problem over the set of common fixed points of an infinite family of nonexpansive mappings on a real reflexive and strictly convex Banach space with a uniformly Gâteaux differentiable norm, we introduce two new implicit iteration methods. Their strong convergence is proved, by using new V-mappings instead of W-ones.     

Tikhonov regularization method for a system of equilibrium problems in Banach spaces

The purpose of this paper is to investigate the Tikhonov regularization method for solving a system of ill-posed equilibrium problems in Banach spaces with a posteriori regularization-parameter choice. An application to convex minimization problems with coupled constraints is also given.     

A steepest-descent Krasnosel’skii–Mann algorithm for a class of variational inequalities in Banach spaces

In this paper, in order to solve a variational inequality problem over the fixed point set of a nonexpansive mapping on uniformly smooth or reflexive and strictly convex Banach spaces with a uniformly Gâteaux differentiable norm, we investigate an explicit iteration method, based on the steepest-descent and Krasnosel’skii–Mann algorithms. We also show that some modifications of the last and Halpern-type algorithms are special cases of our result.     

A new explicit iteration method for a class of variational inequalities

In this paper, we propose a new simple explicit iterative algorithm to find a solution for variational inequalities over the set of common fixed points of an infinite family of nonexpansive mappings on real reflexive and strictly convex Banach spaces with a uniformly Gâteaux differentiable norm. Two numerical examples also are given for illustration.     

Iterative methods for a class of variational inequalities in Hilbert spaces

In this paper, we introduce implicit and explicit iterative methods for solving a variational inequality problem over the set of zeros for a maximal monotone mapping in Hilbert spaces. As consequence, new modifications of the proximal point method are obtained.     

Discrepancy Principle and Convergence Rates in Regularization of Monotone Ill-Posed Problems

The convergence rates of the regularized solution as well as its Galerkin approximations for nonlinear monotone ill-posed problems in a Banach space are established on the basis of the choice of a regularization parameter by the Morozov discrepancy principle.     

Regularization extragradient method for Lipschitz continuous mappings and inverse strongly-monotone mappings in Hilbert spaces

The purpose of this paper is to present a regularization variant of the extragradient method for finding a common element of the solution sets for a variational inequality problem involving a -Lipschitz continuous monotone mapping A and for a finite family of λ _i -inverse strongly-monotone operators {A _i } _{i = 1} ^N from a closed convex subset K into the Hilbert space H. This article was submitted by the author in English.