Related papers: Extrapolation and Local Acceleration of an Iterati…
When proving the correctness of a method for slicing probabilistic programs, it was previously discovered by the authors that for a fixed point iteration to work one needs a non-standard starting point for the iteration. This paper presents…
Let $T$ be a bounded linear operator on a Hilbert space. Then the Aluthge transform $\Delta T$ and the sequence $(\Delta^nT)$ of Aluthge iterates of $T$ are defined by \begin{align*} \Delta…
We associate to each iterated function system consisting of phi-max-contractions an operator (on the space of continuous functions from the shift space on the metric space corresponding to the system) having a unique fixed point whose image…
We consider a class of nonsmooth fractional programming problems with fixed-point constraints, where the numerator is convex and the denominator is concave. To solve this problem, we propose splitting algorithms that compute subgradient…
This paper proposes an accelerated proximal point method for maximally monotone operators. The proof is computer-assisted via the performance estimation problem approach. The proximal point method includes various well-known convex…
A large literature specifies conditions under which the information complexity for a sequence of numerical problems defined for dimensions $1, 2, \ldots$ grows at a moderate rate, i.e., the sequence of problems is tractable. Here, we focus…
Addressing large-scale indefinite least squares (ILS) problem poses notable computational bottlenecks in the field of numerical linear algebra. State-of-the-art iterative schemes for such problems are predominantly constructed upon the…
In this paper we explore acceleration techniques for large scale nonconvex optimization problems with special focuses on deep neural networks. The extrapolation scheme is a classical approach for accelerating stochastic gradient descent for…
We introduce a new iterative method for computing solutions of elliptic equations with random rapidly oscillating coefficients. Similarly to a multigrid method, each step of the iteration involves different computations meant to address…
In this article, we propose and study a stochastic and relaxed preconditioned Douglas--Rachford splitting method to solve saddle-point problems that have separable dual variables. We prove the almost sure convergence of the iteration…
This paper is devoted to the problem of finding a common fixed point of quasinonexpansive mappings defined on a Hilbert space. To approximate the solution to this problem, we present several iterative processes using the parallel method…
Operator splitting methods tailored to coupled linear port-Hamiltonian systems are developed. We present algorithms that are able to exploit scalar coupling, as well as multirate potential of these coupled systems. The obtained algorithms…
We show that sampling or interpolation formulas in reproducing kernel Hilbert spaces can be obtained by reproducing kernels whose dual systems form molecules, ensuring that the size profile of a function is fully reflected by the size…
In this paper we study the relaxed primal-dual algorithm for solving composite monotone inclusions in real Hilbert spaces with critical preconditioners. Our approach is based in new results on the asymptotic behaviour of…
In this paper, we consider a non-convex problem which is the sum of $\ell_0$-norm and a convex smooth function under box constraint. We propose one proximal iterative hard thresholding type method with extrapolation step used for…
The discretization of least-squares problems for linear ill-posed operator equations in Hilbert spaces is considered. The main subject of this article concerns conditions for convergence of the associated discretized minimum-norm…
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 propose basic and natural assumptions under which iterative optimization methods with compressed iterates can be analyzed. This problem is motivated by the practice of federated learning, where a large model stored in the cloud is…
In this paper we discuss some properties of resolvents of an accretive operator in linear 2-normed spaces, focusing on the concept of contraction mapping and the unique fixed point of contraction mappings in linear 2- normed spaces. Also,…
Fixed-point iteration algorithms like RTA (response time analysis) and QPA (quick processor-demand analysis) are arguably the most popular ways of solving schedulability problems for preemptive uniprocessor FP (fixed-priority) and EDF…