Related papers: Weak Convergence for Variational Inequalities with…
Incremental methods are widely utilized for solving finite-sum optimization problems in machine learning and signal processing. In this paper, we study a family of incremental methods -- including incremental subgradient, incremental…
This paper deals with a modified iterative projection method for approximating a solution of the hierarchical fixed point problem for a sequene of nearly nonexpansive mappings with respect to a nonexpansive mapping. It is shown that under…
Variational inequalities play a key role in machine learning research, such as generative adversarial networks, reinforcement learning, adversarial training, and generative models. This paper is devoted to the constrained variational…
This survey reviews variational and iterative methods for reconstructing non-negative solutions of ill-posed problems in infinite-dimensional spaces. We focus on two classes of methods: variational methods based on entropy-minimization or…
In this work, we characterize the existence of solution for a certain variational inequality by means of a classical minimax theorem. In addition, we propose a numerical algorithm for the solution of an inverse problem associated with a…
This paper deals with a modifed iterative projection method for approximating a solution of hierarchical fixed point problems for nearly nonexpansive mappings. Some strong convergence theorems for the proposed method are presented under…
Fixed point iterations are a fundamental tool in numerical analysis and scientific computing for the approximation of solutions to nonlinear problems. Their convergence is often established via the Banach fixed point theorem, provided that…
In this paper, we introduce a new method for solving variational inequality problems with monotone and Lipschitz-continuous mapping in Hilbert space. The iterative process is based on two well-known projection method and the hybrid (or…
The theory of matrix splitting is a useful tool for finding solution of rectangular linear system of equations, iteratively. The purpose of this paper is two-fold. Firstly, we revisit theory of weak regular splittings for rectangular…
We propose and study a strongly convergent inexact inertial projective splitting (PS) algorithm for finding zeros of composite monotone inclusion problems involving the sum of finitely many maximal monotone operators. Strong convergence of…
An adaptive proximal method for a special class of variational inequalities and related problems is proposed. For example, the so-called mixed variational inequalities and composite saddle problems are considered. Some estimates of the…
This paper is concerned with some new projection methods for solving variational inequality problems with monotone and Lipschitz-continuous mapping in Hilbert space. First, we propose the projected reflected gradient algorithm with a…
We establish a novel convergent iteration framework for a weak approximation of general switching diffusion. The key theoretical basis of the proposed approach is a restriction of the maximum number of switching so as to untangle and…
We study the weak finite element method solving convection-diffusion equations. A weak finite element scheme is presented based on a spacial variational form. We established a weak embedding inequality that is very useful in the weak finite…
In these notes we propose and analyze an inertial type method for obtaining stable approximate solutions to nonlinear ill-posed operator equations. The method is based on the Levenberg-Marquardt (LM) iteration. The main obtained results…
This work provides some general theorems about unconditional and conditional weak convergence of empirical processes in the case of Poisson sampling designs. The theorems presented in this work are stronger than previously published…
We introduce a penalty term-based splitting algorithm with inertial effects designed for solving monotone inclusion problems involving the sum of maximally monotone operators and the convex normal cone to the (nonempty) set of zeros of a…
In this paper, we introduce and study a new extragradient iterative process for finding a common element of the set of fixed points of an infinite family of nonexpansive mappings and the set of solutions of a variational inequality for an…
We propose inertial versions of block coordinate descent methods for solving non-convex non-smooth composite optimization problems. Our methods possess three main advantages compared to current state-of-the-art accelerated first-order…
Basing on some recently proposed methods for solving variational inequalities with non-smooth operators, we propose an analogue of the Mirror Prox method for the corresponding class of problems under the assumption of relative smoothness…