Related papers: Relocated Fixed-Point Iterations with Applications…

This paper proposes a data-driven approach for constructing firmly nonexpansive operators. We demonstrate its applicability in Plug-and-Play (PnP) methods, where classical algorithms such as Forward-Backward splitting, Chambolle-Pock…

In this paper, we develop a new type of accelerated algorithms to solve some classes of maximally monotone equations as well as monotone inclusions. Instead of using Nesterov's accelerating approach, our methods rely on a so-called…

Adam is a popular variant of stochastic gradient descent for finding a local minimizer of a function. In the constant stepsize regime, assuming that the objective function is differentiable and non-convex, we establish the convergence in…

In this paper, we study the nonexpansive properties of a generalized forward-backward splitting (G-FBS) operator, particularly under the setting of degenerate metric, from which follow the convergence results in terms of degenerate metric…

We consider the problem of finding the minimizations of the sum of two convex functions and the composition of another convex function with a continuous linear operator from the view of fixed point algorithms based on proximity operators,…

We study the discrete dynamical system obtained by repeatedly applying the Pearson correlation operator to a real matrix. Each step centers every row, normalizes each centered row to unit Euclidean norm, and forms the Gram matrix of the…

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…

This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…

The paper studies decentralized optimization over networks, where agents minimize a composite objective consisting of the sum of smooth convex functions--the agents' losses--and an additional nonsmooth convex extended value function. We…

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…

In [C.W. Gear, T.J. Kaper, I.G. Kevrekidis, and A. Zagaris, Projecting to a Slow Manifold: Singularly Perturbed Systems and Legacy Codes, SIAM J. Appl. Dyn. Syst. 4 (2005) 711-732], we developed a class of iterative algorithms within the…

We consider the problem of finding a fixed point of a nonexpansive mapping, which is also a solution of a pseudo-monotone equilibrium problem, where the bifunction in the equilibrium problem is the sum of two ones. We propose a splitting…

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…

We shed light on the structure of the "three-operator" version of the forward-Douglas--Rachford splitting algorithm for finding a zero of a sum of maximally monotone operators $A + B + C$, where $B$ is cocoercive, involving only the…

Multi-block separable convex problems recently received considerable attention. This class of optimization problems minimizes a separable convex objective function with linear constraints. The algorithmic challenges come from the fact that…

Iterative algorithms are instrumental in modern numerical simulation for solving systems arising from the discretization of PDEs. They face however significant challenges in industrial applications, such as slow convergence, limit cycle…

In this work, we address a class of nonconvex nonsmooth optimization problems where the objective function is the sum of two smooth functions (one of which is proximable) and two nonsmooth functions (one proper, closed and proximable, and…

Deep neural networks, despite their success in numerous applications, often function without established theoretical foundations. In this paper, we bridge this gap by drawing parallels between deep learning and classical numerical analysis.…

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…

The goal of this paper is to study approaches to bridge the gap between first-order and second-order type methods for composite convex programs. Our key observations are: i) Many well-known operator splitting methods, such as…