Related papers: Acceleration methods for fixed point iterations
We propose a variation of the forward--backward splitting method for solving structured monotone inclusions. Our method integrates past iterates and two deviation vectors into the update equations. These deviation vectors bring flexibility…
In this paper, we introduce and study a new extragradient iterative process for finding a common element of the set of fixed points of an infinite family of nonexpansive mappings and the set of solutions of a variational inequality for an…
This paper describes and establishes the iteration-complexity of a doubly accelerated inexact proximal point (D-AIPP) method for solving the nonconvex composite minimization problem whose objective function is of the form $f+h$ where $f$ is…
The purpose of this paper is to study the influence of relaxation and acceleration techniques on the convergence behavior of the non-overlapping Schwarz algorithm with alternating Dirichlet-Neumann transmission conditions in the context of…
Sample average approximation (SAA) is a technique for obtaining approximate solutions to stochastic programs that uses the average from a random sample to approximate the expected value that is being optimized. Since the outcome from…
Recent efforts on solving inverse problems in imaging via deep neural networks use architectures inspired by a fixed number of iterations of an optimization method. The number of iterations is typically quite small due to difficulties in…
Inverse problems consist of recovering a signal from a collection of noisy measurements. These problems can often be cast as feasibility problems; however, additional regularization is typically necessary to ensure accurate and stable…
We establish linear convergence rates for a certain class of extrapolated fixed point algorithms which are based on dynamic string-averaging methods in a real Hilbert space. This applies, in particular, to the extrapolated simultaneous and…
For optimal power flow problems with chance constraints, a particularly effective method is based on a fixed point iteration applied to a sequence of deterministic power flow problems. However, a priori, the convergence of such an approach…
This work blends the inexact Newton method with iterative combined approximations (ICA) for solving topology optimization problems under the assumption of geometric nonlinearity. The density-based problem formulation is solved using a…
We give a complete characterization of the behavior of the Anderson acceleration (with arbitrary nonzero mixing parameters) on linear problems. Let n be the grade of the residual at the starting point with respect to the matrix defining the…
In this article, we establish a class of new accelerated modulus-based iteration methods for solving the linear complementarity problem. When the system matrix is an $H_+$-matrix, we present appropriate criteria for the convergence…
Convex sparsity-inducing regularizations are ubiquitous in high-dimensional machine learning, but solving the resulting optimization problems can be slow. To accelerate solvers, state-of-the-art approaches consist in reducing the size of…
We present abstract acceleration techniques for computing loop invariants for numerical programs with linear assignments and conditionals. Whereas abstract interpretation techniques typically over-approximate the set of reachable states…
In recent years, convolutional neural networks (CNNs) have shown great performance in various fields such as image classification, pattern recognition, and multi-media compression. Two of the feature properties, local connectivity and…
This paper develops a new class of nonlinear acceleration algorithms based on extending conjugate residual-type procedures from linear to nonlinear equations. The main algorithm has strong similarities with Anderson acceleration as well as…
When used to accelerate the convergence of fixed-point iterative methods, such as the Picard method, which is a kind of nonlinear fixed-point iteration, polynomial extrapolation techniques can be very effective. The numerical solution of…
We establish linear convergence of relocated fixed-point iterations as introduced by Atenas et al. (2025) assuming the algorithmic operator satisfies a linear error bound. In particular, this framework applies to the setting where the…
The computing industry is forced to find alternative design approaches and computing platforms to sustain increased power efficiency, while providing sufficient performance. Among the examined solutions, Approximate Computing, Hardware…
This article generalizes a recently introduced procedure to solve nonlinear systems of equations, radically departing from the conventional Newton-Raphson scheme. The original nonlinear system is first unfolded into three simpler…