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We study a fixed point iterative method based on generalized relaxation of strictly quasi-nonexpansive operators. The iterative method is assembled by averaging of strings, and each string is composed of finitely many strictly…

Optimization and Control · Mathematics 2021-05-03 Touraj Nikazad , Mahdi Mirzapour

The purpose of this paper is to propose and analyze a multi-step iterative algorithm to solve a convex optimization problem and a fixed point problem posed on a Hadamard space. The convergence properties of the proposed algorithm are…

Functional Analysis · Mathematics 2018-02-28 Muhammad Aqeel Ahmad Khan , Hafiza Arham Maqbool

A broad range of inverse problems can be abstracted into the problem of minimizing the sum of several convex functions in a Hilbert space. We propose a proximal decomposition algorithm for solving this problem with an arbitrary number of…

Optimization and Control · Mathematics 2009-11-13 Patrick L. Combettes , Jean-Christophe Pesquet

The problem of minimizing the sum of nonsmooth, convex objective functions defined on a real Hilbert space over the intersection of fixed point sets of nonexpansive mappings, onto which the projections cannot be efficiently computed, is…

Optimization and Control · Mathematics 2016-02-08 Hideaki Iiduka

Let $Q$ be a nonempty closed and convex subset of a real Hilbert space $% \mathcal{H}$, $S:Q\rightarrow Q$ a nonexpansive mapping, $A:Q\rightarrow Q$ an inverse strongly monotone operator, and $f:Q\rightarrow Q$ a contraction mapping. We…

Dynamical Systems · Mathematics 2022-09-22 Ramzi May

The paper investigates two inertial extragradient algorithms for seeking a common solution to a variational inequality problem involving a monotone and Lipschitz continuous mapping and a fixed point problem with a demicontractive mapping in…

Optimization and Control · Mathematics 2023-08-08 Bing Tan , Liya Liu , Xiaolong Qin

We consider the variational inequality problem over the intersection of fixed point sets of firmly nonexpansive operators. In order to solve the problem, we present an algorithm and subsequently show the strong convergence of the generated…

Optimization and Control · Mathematics 2020-01-30 Mootta Prangprakhon , Nimit Nimana , Narin Petrot

We leverage the connections between nonexpansive maps, monotone Lipschitz operators, and proximal mappings to obtain near-optimal (i.e., optimal up to poly-log factors in terms of iteration complexity) and parameter-free methods for solving…

Optimization and Control · Mathematics 2020-04-14 Jelena Diakonikolas

In this work, we develop a convergence framework for iterative algorithms whose updates can be described by a one-parameter family of nonexpansive operators. Within the framework, each step involving one of the main algorithmic operators is…

Optimization and Control · Mathematics 2025-12-01 Felipe Atenas , Heinz H. Bauschke , Minh N. Dao , Matthew K. Tam

Fixed point iterations play a central role in the design and the analysis of a large number of optimization algorithms. We study a new iterative scheme in which the update is obtained by applying a composition of quasinonexpansive operators…

Optimization and Control · Mathematics 2017-08-15 Patrick L. Combettes , Lilian E. Glaudin

In this paper by using $W_{n}$-mapping, we introduce a composite iterative method for finding a common fixed point for infinite family of nonexpansive mappings and a solution of a certain variational inequality. Furthermore, the strong…

Functional Analysis · Mathematics 2013-08-19 Vahid Darvish , S. M. Vaezpour

We propose an abstract stochastic scheme for solving a broad range of monotone operator inclusion problems in Hilbert spaces. This framework allows for the introduction of stochasticity at several levels in monotone operator splitting…

Optimization and Control · Mathematics 2026-02-13 Patrick L. Combettes , Javier I. Madariaga

Building up on classical linear formulations, we posit that a broad class of problems in signal synthesis and in signal recovery are reducible to the basic task of finding a point in a closed convex subset of a Hilbert space that satisfies…

Optimization and Control · Mathematics 2021-05-18 Patrick L. Combettes , Zev C. Woodstock

Iterative algorithms are fundamental tools for approximating fixed-points of nonexpansive operators in real Hilbert spaces. Among them, Krasnosel'ski\u{\i}--Mann iteration and Halpern iteration are two widely used schemes. In this work, we…

Optimization and Control · Mathematics 2026-02-20 Yifan Bai , Yantao Li , Jian Yu , Jingwei Liang

In this article, we derive an iterative scheme through a quasi-Newton technique to capture robust weakly efficient points of uncertain multiobjective optimization problems under the upper set less relation. It is assumed that the set of…

Optimization and Control · Mathematics 2025-05-21 K. Gupta , D. Ghosh , C. Tammer , X. Zhao , J. C. Yao

A generalization of a viscosity generalized Halpern iteration scheme is analyzed. It is proven that the solution converges asymptotically strongly to a unique fixed point of an asymptotically nonexpansive mapping which drives the iteration…

Functional Analysis · Mathematics 2009-02-18 M. De la Sen

In this article a unified approach to iterative soft-thresholding algorithms for the solution of linear operator equations in infinite dimensional Hilbert spaces is presented. We formulate the algorithm in the framework of generalized…

Functional Analysis · Mathematics 2010-10-26 Kristian Bredies , Dirk A. Lorenz

This paper is to analyze the approximation solution of a split variational inclusion problem in the framework of infinite dimensional Hilbert spaces. For this purpose, several inertial hybrid and shrinking projection algorithms are proposed…

Optimization and Control · Mathematics 2024-09-17 Zheng Zhou , Bing Tan , Songxiao Li

By using the Ishikawa iterative algorithm, we approximate the fixed points and the best proximity points of a relatively non expansive mapping. Also, we use the von Neumann sequence to prove the convergence result in a Hilbert space…

Functional Analysis · Mathematics 2020-05-13 V. Pragadeeswarar , R. Gopi , Choonkil Park , Dong Yun Shin

A numerical algorithm for solving mantle convection problems with strongly variable viscosity is presented. Equations for conservation of mass and momentum for highly viscous and incompressible fluids are solved iteratively by a multigrid…

Geophysics · Physics 2009-11-10 Masanori Kameyama , Akira Kageyama , Tetsuya Sato