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In this study, we introduce a new iterative processes to approximate common fixed points of an infinite family of quasi-nonexpansive mappings and obtain a strongly convergent iterative sequence to the common fixed points of these mappings…

Functional Analysis · Mathematics 2015-02-24 K. Dogan , V. Karakaya

We consider nonlinear inverse problems described by operator equations in Banach spaces. Assuming conditional stability of the inverse problem, that is, assuming that stability holds on a closed, convex subset of the domain of the operator,…

Numerical Analysis · Mathematics 2012-06-19 Maarten V. de Hoop , Lingyun Qiu , Otmar Scherzer

Variational source conditions proved useful for deriving convergence rates for Tikhonov's regularization method and also for other methods. Up to now such conditions have been verified only for few examples or for situations which can be…

Numerical Analysis · Mathematics 2017-09-19 Jens Flemming

Landweber-type methods are prominent for solving ill-posed inverse problems in Banach spaces and their convergence has been well-understood. However, how to derive their convergence rates remains a challenging open question. In this paper,…

Numerical Analysis · Mathematics 2024-11-15 Qinian Jin

Let $X$ be a real Banach space with a normalized duality mapping uniformly norm-to-weak$^\star$ continuous on bounded sets or a reflexive Banach space which admits a weakly continuous duality mapping $J_{\Phi}$ with gauge $\phi$. Let $f$ be…

Optimization and Control · Mathematics 2007-12-10 Jean-Philippe Chancelier

In recent years, accelerated extra-gradient methods have attracted much attention by researchers, for solving monotone inclusion problems. A limitation of most current accelerated extra-gradient methods lies in their direct utilization of…

Optimization and Control · Mathematics 2025-03-24 Ya-xiang Yuan , Yi Zhang

In this article, we develop an algorithm suitable for constrained optimization in $\mathbb{R}^n$. The results are developed through standard tools of n-dimensional real analysis and basic concepts of optimization. Indeed, the well known…

Optimization and Control · Mathematics 2019-02-26 Fabio Botelho

The extragradient (EG), introduced by G. M. Korpelevich in 1976, is a well-known method to approximate solutions of saddle-point problems and their extensions such as variational inequalities and monotone inclusions. Over the years,…

Optimization and Control · Mathematics 2023-03-31 Quoc Tran-Dinh

In the Normed space theory, the existence of fixed points is one of the main tools in improving efficiency of iterative algorithms in optimization, numerical analysis and various mathematical applications. This study introduces and…

Optimization and Control · Mathematics 2024-05-15 Akansha Tyagi , Sachin Vashistha

In this paper, we introduce a new hybrid algorithm for solving equilibrium problems. The algorithm combines the extragradient method and the hybrid (outer approximation) method. In this algorithm, only an optimization program is solved at…

Optimization and Control · Mathematics 2015-10-29 Dang Van Hieu

In this paper, we study a class of generalized monotone variational inequality (GMVI) problems whose operators are not necessarily monotone (e.g., pseudo-monotone). We present non-Euclidean extragradient (N-EG) methods for computing…

Optimization and Control · Mathematics 2013-11-13 Cong D. Dang , Guanghui Lan

A Strong Convergence Theorem for finite families of Bregman Demimetric Mappings in a Banach Space under a New Shrinking projection Method

Functional Analysis · Mathematics 2021-09-07 Bijan Orouji , Ebrahim Soori , Donal O'Regan , Ravi P. Agarwal

We develop a general, functional calculus approach to approximation of $C_0$-semigroups on Banach spaces by bounded completely monotone functions of their generators. The approach comprises most of well-known approximation formulas, yields…

Functional Analysis · Mathematics 2018-07-10 A. Gomilko , S. Kosowicz , Yu. Tomilov

In this paper, we propose a globally convergent method for solving constrained nonlinear systems. The method combines an efficient Newton conditional gradient method with a derivative-free and nonmonotone linesearch strategy. The global…

Optimization and Control · Mathematics 2018-06-06 M. L. N. Gonçalves , F. R. Oliveira

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…

Optimization and Control · Mathematics 2015-01-30 Yu. V. Malitsky , V. V. Semenov

We show that fractional powers of general sectorial operators on Banach spaces can be obtained by the harmonic extension approach. Moreover, for the corresponding second order ordinary differential equation with incomplete data describing…

Functional Analysis · Mathematics 2020-09-08 Jan Meichsner , Christian Seifert

This work introduces a new general approach for the numerical analysis of stable equilibria to second order mean field games systems in cases where the uniqueness of solutions may fail. For the sake of simplicity, we focus on a simple…

Analysis of PDEs · Mathematics 2024-10-30 Jules Berry , Olivier Ley , Francisco J Silva

We consider the method of alternating (metric) projections for pairs of linear subspaces of finite dimensional Banach spaces. We investigate the size of the set of points for which this method converges to the metric projection onto the…

Functional Analysis · Mathematics 2023-06-01 Christian Bargetz , Franz Luggin

In this work, we introduce two algorithmic frameworks, named Bregman extragradient method and Bregman extrapolation method, for solving saddle point problems. The proposed frameworks not only include the well-known extragradient and…

Optimization and Control · Mathematics 2021-08-26 Hui Zhang

We propose a forward-backward splitting algorithm based on Bregman distances for composite minimization problems in general reflexive Banach spaces. The convergence is established using the notion of variable quasi-Bregman monotone…

Optimization and Control · Mathematics 2016-10-10 Quang Van Nguyen