Related papers: Relaxed Fixed Point Iterations for Matrix Equation…
We develop fixed-point algorithms for the approximation of structured matrices with rank penalties. In particular we use these fixed-point algorithms for making approximations by sums of exponentials, or frequency estimation. For the basic…
Solving linear systems is a ubiquitous task in science and engineering. Because directly inverting a large-scale linear system can be computationally expensive, iterative algorithms are often used to numerically find the inverse. To…
The following paper compares a consistent Newton-Raphson and fixed-point iteration based solution strategy for a variational multiscale finite element formulation for incompressible Navier-Stokes. The main contributions of this work include…
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…
The matrix rank minimization problem has applications in many fields such as system identification, optimal control, low-dimensional embedding, etc. As this problem is NP-hard in general, its convex relaxation, the nuclear norm minimization…
With the ever increasing computational power available and the development of high-performances computing, investigating the properties of realistic very large-scale nonlinear dynamical systems has been become reachable. It must be noted…
We study the convergence of random function iterations for finding an invariant measure of the corresponding Markov operator. We call the problem of finding such an invariant measure the stochastic fixed point problem. This generalizes…
The three-step alternating iteration scheme for finding an iterative solution of a singular (non-singular) linear systems in a faster way was introduced by Nandi {\it et al.} [Numer. Algorithms; 84 (2) (2020) 457-483], recently. The authors…
In this paper, we introduce a new iterative method to find a common solution of a generalized mixed equilibrium problem, a variational inequality problem and a hierarchical fixed point problem for a demicontinuous nearly nonexpansive…
We present a form of stratified MCMC algorithm built with non-reversible stochastic dynamics in mind. It can also be viewed as a generalization of the exact milestoning method, or form of NEUS. We prove convergence of the method under…
This paper discusses algorithms for solving Markov decision processes (MDPs) that have monotone optimal policies. We propose a two-stage alternating convex optimization scheme that can accelerate the search for an optimal policy by…
Two adaptive relaxation strategies are proposed for Anderson acceleration. They are specifically designed for applications in which mappings converge to a fixed point. Their superiority over alternative Anderson acceleration is demonstrated…
Although the Kadanoff-Baym equations are typically solved using time-stepping methods, iterative global-in-time solvers offer potential algorithmic advantages, particularly when combined with compressed representations of two-time objects.…
In this paper, we study a nonconvex continuous relaxation of MAP inference in discrete Markov random fields (MRFs). We show that for arbitrary MRFs, this relaxation is tight, and a discrete stationary point of it can be easily reached by a…
In this paper, we extend the improved pointwise iteration-complexity result of a dynamic regularized alternating direction method of multipliers (ADMM) for a new stepsize domain. In this complexity analysis, the stepsize parameter can even…
This note considers the momentum method by Polyak and the accelerated gradient method by Nesterov, both without line search but with fixed step length applied to strictly convex quadratic functions assuming that exact gradients are used and…
In this paper we analyse convergence of projected fixed-point iteration on a Riemannian manifold of matrices with fixed rank. As a retraction method we use `projector splitting scheme'. We prove that the projector splitting scheme converges…
This paper is concerned with the study of a family of fixed point iterations combining relaxation with different inertial (acceleration) principles. We provide a systematic, unified and insightful analysis of the hypotheses that ensure…
As first-order optimization methods become the method of choice for solving large-scale optimization problems, optimization solvers based on first-order algorithms are being built. Such general-purpose solvers must robustly detect…
We study a general class of bilevel problems, consisting in the minimization of an upper-level objective which depends on the solution to a parametric fixed-point equation. Important instances arising in machine learning include…