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In the framework of a real Hilbert space we consider the problem of approaching solutions to a class of hierarchical variational inequality problems, subsuming several other problem classes including certain mathematical programs under…

Optimization and Control · Mathematics 2026-01-27 Pavel Dvurechensky , Meggie Marschner , Shimrit Shtern , Mathias Staudigl

Given a Hilbert space and a finite family of operators defined on the space, the common fixed point problem (CFPP) is to find a point in the intersection of the fixed point sets of these operators. Instances of the problem have numerous…

Optimization and Control · Mathematics 2025-09-05 Yair Censor , Daniel Reem , Maroun Zaknoon

In this paper, we analyze the iteration-complexity of Generalized Forward--Backward (GFB) splitting algorithm, as proposed in \cite{gfb2011}, for minimizing a large class of composite objectives $f + \sum_{i=1}^n h_i$ on a Hilbert space,…

Optimization and Control · Mathematics 2014-02-11 Jingwei Liang , Jalal M. Fadili , Gabriel Peyré

Our aim is to present several properties of a Landweber operator and of a Landweber-type operator. These operators are widely used in methods for solving the split feasibility problem and the split common fixed point problem. The presented…

Optimization and Control · Mathematics 2014-11-10 Andrzej Cegielski

We provide new complexity information for the convergence of the Hybrid Steepest Descent Method for solving the Variational Inequality Problem for a strict contraction on Hilbert space over a closed convex set C given either as the fixed…

Logic · Mathematics 2016-10-04 Daniel Körnlein

We introduce and study the Split Common Null Point Problem (SCNPP) for set-valued maximal monotone mappings in Hilbert spaces. This problem generalizes our Split Variational Inequality Problem (SVIP) [Y. Censor, A. Gibali and S. Reich,…

Optimization and Control · Mathematics 2012-04-17 Charles Byrne , Yair Censor , Aviv Gibali , Simeon Reich

In this paper we study iterative algorithms for finding a common element of the set of fixed points of $\kappa$-strict pseudocontractions or finding a solution of a variational inequality problem for a monotone, Lipschitz continuous…

Optimization and Control · Mathematics 2007-12-05 Jean-Philippe Chancelier

Proper splittings of operators are commonly used to study the convergence of iterative processes. In order to approximate solutions of operator equations, in this article we deal with proper splittings of closed range bounded linear…

Functional Analysis · Mathematics 2024-03-18 Guillermina Fongi , María Celeste Gonzalez

In this paper, we introduce two novel parallel projection methods for finding a solution of a system of variational inequalities which is also a common fixed point of a family of (asymptotically) $\kappa$ - strict pseudocontractive…

Optimization and Control · Mathematics 2015-11-09 Dang Van Hieu

The forward-backward splitting algorithm is a popular operator-splitting method for solving monotone inclusion of the sum of a maximal monotone operator and a cocoercive operator. In this paper, we present a new convergence analysis of a…

Functional Analysis · Mathematics 2019-08-30 Fuying Cui , Yuchao Tang , Chuanxi Zhu

In this paper, we study $\Delta$- convergence of iterations for a sequence of strongly quasi-nonexpansive mappings as well as the strong convergence of the Halpern type regularization of them in Hadamard spaces. Then, we give some their…

Functional Analysis · Mathematics 2016-11-10 Hadi Khatibzadeh , Vahid Mohebbi

A parallel splitting method is proposed for solving systems of coupled monotone inclusions in Hilbert spaces. Convergence is established for a wide class of coupling schemes. Unlike classical alternating algorithms, which are limited to two…

Optimization and Control · Mathematics 2009-02-26 H. Attouch , L. M. Briceno-Arias , P. L. Combettes

In the setting of CAT(k) spaces, common fixed point iterations built from prox mappings (e.g. prox-prox, Krasnoselsky-Mann relaxations, nonlinear projected-gradients) converge locally linearly under the assumption of linear metric…

Optimization and Control · Mathematics 2021-12-13 Florian Lauster , D. Russell Luke

Let $C$ be a nonempty closed and convex subset of a uniformly smooth and uniformly convex real Banach space $E$ with dual space $E^*$. We present a novel hybrid method for finding a common solution of a family of equilibrium problems, a…

Functional Analysis · Mathematics 2022-08-17 Markjoe O. Uba , Maria A. Onyido , Cyril I. Udeani , Peter U. Nwokoro

Recently, Krukier et al. [Generalized skew-Hermitian triangular splitting iteration methods for saddle-point linear systems, Numer. Linear Algebra Appl. 21 (2014) 152-170] proposed an efficient generalized skew-Hermitian triangular…

Numerical Analysis · Mathematics 2014-02-25 Yan Dou , Ai-Li Yang , Yu-Jiang Wu

Numerous problems in signal processing and imaging, statistical learning and data mining, or computer vision can be formulated as optimization problems which consist in minimizing a sum of convex functions, not necessarily differentiable,…

Optimization and Control · Mathematics 2017-12-12 Abdellatif Moudafi , Aviv Gibali

We study the convergence of random function iterations for finding an invariant measure of the corresponding Markov operator. We call the problem of finding such an invariant measure the stochastic fixed point problem. This generalizes…

Optimization and Control · Mathematics 2024-04-16 Neal Hermer , D. Russell Luke , Anja Sturm

In the present paper, a robust approach to a special class of convex feasibility problems is considered. By techniques of convex and variational analysis, conditions for the existence of robust feasible solutions and related error bounds…

Optimization and Control · Mathematics 2025-05-06 Amos Uderzo

We introduce a relaxed-projection splitting algorithm for solving variational inequalities in Hilbert spaces for the sum of nonsmooth maximal monotone operators, where the feasible set is defined by a nonlinear and nonsmooth continuous…

Optimization and Control · Mathematics 2015-12-31 J. Y. Bello Cruz , R. Diaz Millan

This paper is concerned with convex composite minimization problems in a Hilbert space. In these problems, the objective is the sum of two closed, proper, and convex functions where one is smooth and the other admits a computationally…

Optimization and Control · Mathematics 2020-02-19 Patrick R. Johnstone , Pierre Moulin