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In this paper, we propose two novel inertial-like algorithms for solving the split common null point problem (SCNPP) with respect to set-valued maximal operators. The features of the presented algorithm are using new inertial structure…

Numerical Analysis · Mathematics 2021-09-21 Yan Tang , Shiqing Zhang

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

We introduce a new extragradient iterative process, motivated and inspired by [S. H. Khan, A Picard-Mann Hybrid Iterative Process, Fixed Point Theory and Applications, doi:10.1186/1687-1812-2013-69], for finding a common element of the set…

Functional Analysis · Mathematics 2014-03-14 Ibrahim Karahan , Murat Ozdemir

In this paper we consider the computation of approximate solutions for inverse problems in Hilbert spaces. In order to capture the special feature of solutions, non-smooth convex functions are introduced as penalty terms. By exploiting the…

Numerical Analysis · Mathematics 2015-06-18 Qinian Jin , Xiliang Lu

The aim of this article is to introduce an iterative algorithm for finding a common solution from the set of an equilibrium point for a bifunction and the set of a singularity of an inclusion problem on an Hadamard manifold. We also discuss…

Functional Analysis · Mathematics 2019-07-02 Konrawut Khammahawong , Poom Kumam , Parin Chaipunya

The three-operators splitting algorithm is a popular operator splitting method for finding the zeros of the sum of three maximally monotone operators, with one of which is cocoercive operator. In this paper, we propose a class of inertial…

Optimization and Control · Mathematics 2019-08-30 Fuying Cui , Yuchao Tang , Yang Yang

We consider the primal problem of finding the zeros of the sum of a maximally monotone operator with the composition of another maximally monotone operator with a linear continuous operator and a corresponding dual problem formulated by…

Optimization and Control · Mathematics 2012-06-27 Radu Ioan Bot , Ernö Robert Csetnek , Andre Heinrich

Our work presents a new iterative scheme to approximate the fixed points of nonexpansive mapping. The proposed algorithm is constructed to enhance convergence efficiency while preserving theoretical robustness. Under appropriate assumptions…

Functional Analysis · Mathematics 2026-01-12 Nida Izhar Mallick , Izhar Uddin

The principle underlying this paper is the basic observation that the problem of simultaneously solving a large class of composite monotone inclusions and their duals can be reduced to that of finding a zero of the sum of a maximally…

Optimization and Control · Mathematics 2010-11-29 L. Briceno-Arias , P. L. Combettes

Most algorithms for solving optimization problems or finding saddle points of convex-concave functions are fixed-point algorithms. In this work we consider the generic problem of finding a fixed point of an average of operators, or an…

Machine Learning · Computer Science 2020-06-17 Grigory Malinovsky , Dmitry Kovalev , Elnur Gasanov , Laurent Condat , Peter Richtárik

This paper investigates the problem of finding a fixed point for a global nonexpansive operator under time-varying communication graphs in real Hilbert spaces, where the global operator is separable and composed of an aggregate sum of local…

Optimization and Control · Mathematics 2019-11-11 Xiuxian Li , Lihua Xie

The obstacle problem is a class of free boundary problems which finds applications in many disciplines such as porous media, financial mathematics and optimal control. In this paper, we propose two operator-splitting methods to solve the…

Numerical Analysis · Mathematics 2023-02-08 Hao Liu , Dong Wang

In this paper we propose an approach for solving systems of nonlinear equations without computing function derivatives. Motivated by the application area of tomographic absorption spectroscopy, which is a highly-nonlinear problem with…

Optimization and Control · Mathematics 2024-05-15 F. J. Aragón-Artacho , W. Cai , Y. Censor , A. Gibali , C. Shui , D. Torregrosa-Belén

In this paper, first we introduce a new mapping for finding a common fixed point of an infinite family of nonexpansive mappings then we consider iterative method for finding a common element of the set of fixed points of an infinite family…

Functional Analysis · Mathematics 2015-02-18 Vahid Darvish , S. M. Vaezpour

The forward-backward splitting technique is a popular method for solving monotone inclusions that has applications in optimization. In this paper we explore the behaviour of the algorithm when the inclusion problem has no solution. We…

Optimization and Control · Mathematics 2016-08-09 Walaa M. Moursi

Proximal splitting algorithms for monotone inclusions (and convex optimization problems) in Hilbert spaces share the common feature to guarantee for the generated sequences in general weak convergence to a solution. In order to achieve…

Optimization and Control · Mathematics 2017-11-21 Radu Ioan Bot , Ernö Robert Csetnek , Dennis Meier

In this paper we present a variant of the proximal forward-backward splitting iteration for solving nonsmooth optimization problems in Hilbert spaces, when the objective function is the sum of two nondifferentiable convex functions. The…

Optimization and Control · Mathematics 2016-01-13 Jose Yunier Bello Cruz

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, a novel parallel hybrid iterative method is proposed for finding a common element of the set of solutions of a system of equilibrium problems, the set of solutions of variational inequalities for inverse strongly monotone…

Optimization and Control · Mathematics 2015-10-28 Dang Van Hieu

In this paper, we introduce three new iterative methods for finding a common point of the set of fixed points of a symmetric generalized hybrid mapping and the set of solutions of an equilibrium problem in a real Hilbert space. Each method…

Optimization and Control · Mathematics 2018-05-08 Bui Van Dinh , Nguyen Ngoc Hai , Do Sang Kim