[HTML][HTML] Convergence results of forward-backward algorithms for sum of monotone operators in Banach spaces

Y Shehu - Results in Mathematics, 2019 - Springer
It is well known that many problems in image recovery, signal processing, and machine
learning can be modeled as finding zeros of the sum of maximal monotone and Lipschitz …

Strong convergence of the forward–backward splitting method with multiple parameters in Hilbert spaces

Y Wang, F Wang - Optimization, 2018 - Taylor & Francis
Many problems arising from machine learning, signal & image recovery, and compressed
sensing can be casted into a monotone inclusion problem for finding a zero of the sum of …

A variable metric extension of the forward–backward–forward algorithm for monotone operators

BC Vũ - Numerical Functional Analysis and Optimization, 2013 - Taylor & Francis
We propose a variable metric extension of the forward–backward-forward algorithm for
finding a zero of the sum of a maximally monotone operator and a monotone Lipschitzian …

Strong convergence studied by a hybrid type method for monotone operators in a Banach space

H Iiduka, W Takahashi - Nonlinear Analysis: Theory, Methods & …, 2008 - Elsevier
In this paper, we study a strong convergence for monotone operators. We first introduce the
hybrid type algorithm for monotone operators. Next, we obtain a strong convergence …

[PDF][PDF] Modified Tseng's splitting algorithms for the sum of two monotone operators in Banach spaces

J Yang, P Cholamjiak, P Sunthrayuth - AIMS Mathematics, 2021 - aimspress.com
In this work, we introduce two modified Tseng's splitting algorithms with a new nonmonotone
adaptive step size for solving monotone inclusion problem in the framework of Banach …

Zero point problem of accretive operators in Banach spaces

SS Chang, CF Wen, JC Yao - Bulletin of the Malaysian Mathematical …, 2019 - Springer
Splitting methods have recently received much attention due to the fact that many nonlinear
problems arising in applied areas such as image recovery, signal processing and machine …

Strong convergence of forward–reflected–backward splitting methods for solving monotone inclusions with applications to image restoration and optimal control

C Izuchukwu, S Reich, Y Shehu, A Taiwo - Journal of Scientific Computing, 2023 - Springer
In this paper, we propose and study several strongly convergent versions of the forward–
reflected–backward splitting method of Malitsky and Tam for finding a zero of the sum of two …

A reflected forward-backward splitting method for monotone inclusions involving Lipschitzian operators

V Cevher, BC Vũ - Set-valued and Variational analysis, 2021 - Springer
In this paper, we propose a novel splitting method for finding a zero point of the sum of two
monotone operators where one of them is Lipschizian. The weak convergence the method is …

A primal-dual splitting algorithm for finding zeros of sums of maximal monotone operators

RI Bot, ER Csetnek, A Heinrich - SIAM Journal on Optimization, 2013 - SIAM
We consider the primal problem of finding the zeros of the sum of a maximal monotone
operator and the composition of another maximal monotone operator with a linear …

New properties of forward–backward splitting and a practical proximal-descent algorithm

Y Huang, Y Dong - Applied Mathematics and Computation, 2014 - Elsevier
In this paper, we discuss a proximal-descent algorithm for finding a zero of the sum of two
maximal monotone operators in a real Hilbert space. Some new properties of forward …