Related papers: A generalized strong convergence algorithm in the …
This paper presents an improved forward-backward splitting algorithm with two inertial parameters. It aims to find a point in the real Hilbert space at which the sum of a co-coercive operator and a maximal monotone operator vanishes. Under…
For a sequence of uniformly bounded, degenerate semigroups on a Hilbert space, we compare various types of convergences to a limit semigroup. Among others, we show that convergence of the semigroups, or of the resolvents of the generators,…
Projection algorithms are well known for their simplicity and flexibility in solving feasibility problems. They are particularly important in practice due to minimal requirements for software implementation and maintenance. In this work, we…
In this paper, we prove optimal convergence rates results for regularisation methods for solving linear ill-posed operator equations in Hilbert spaces. The result generalises existing convergence rates results on optimality to general…
This paper revisits the principle of uniform convergence in statistical learning, discusses how it acts as the foundation behind machine learning, and attempts to gain a better understanding of the essential problem that current deep…
In this paper, we propose a stochastic forward-backward-forward splitting algorithm and prove its almost sure weak convergence in real separable Hilbert spaces. Applications to composite monotone inclusion and minimization problems are…
The split common fixed-point problem is an inverse problem that consists in finding an element in a fixed-point set such that its image under a bounded linear operator belongs to another fixed-point set. Recently Censor and Segal proposed…
We present a quantum algorithm for systems of (possibly inhomogeneous) linear ordinary differential equations with constant coefficients. The algorithm produces a quantum state that is proportional to the solution at a desired final time.…
The article studies the reiterated homogenization of linear elliptic variational inequalities arising in problems with unilateral constrains. We assume that the coefficients of the equations satisfy and abstract hypothesis covering on each…
In this article, we study the convergence behavior of the regularization-based algorithm for solving the polynomial regression model when both input data and responses are from infinite-dimensional Hilbert spaces. We derive convergence…
In this paper, based on inertial and Tseng's ideas, we propose two projection-based algorithms to solve a monotone inclusion problem in infinite dimensional Hilbert spaces. Solution theorems of strong convergence are obtained under the…
We analyze the convergence of the Conjugate Gradient (CG) method in exact arithmetic, when the coefficient matrix $A$ is symmetric positive semidefinite and the system is consistent. To do so, we diagonalize $A$ and decompose the algorithm…
This paper deals with a method for the approximation of a spectral density function among the solutions of a generalized moment problem a` la Byrnes/Georgiou/Lindquist. The approximation is pursued with respect to the Kullback-Leibler…
We consider hierarchical variational inequality problems, or more generally, variational inequalities defined over the set of zeros of a monotone operator. This framework includes convex optimization over equilibrium constraints and…
The forward-backward splitting algorithm is a popular operator-splitting method for solving monotone inclusion of the sum of a maximal monotone operator and a cocoercive operator. In this paper, we present a new convergence analysis of a…
The RFMP is an iterative regularization method for a class of linear inverse problems. It has proved to be applicable to problems which occur, for example, in the geosciences. In the early publications [Fischer2011] and [FischerMichel2012],…
In this paper we consider a stochastic heavy-ball method for solving linear ill-posed inverse problems. With suitable choices of the step-sizes and the momentum coefficients, we establish the regularization property of the method under {\it…
We consider stochastic variational inequality problems where the mapping is monotone over a compact convex set. We present two robust variants of stochastic extragradient algorithms for solving such problems. Of these, the first scheme…
A parallel splitting method is proposed for solving systems of coupled monotone inclusions in Hilbert spaces. Convergence is established for a wide class of coupling schemes. Unlike classical alternating algorithms, which are limited to two…
We propose a variable metric forward-backward splitting algorithm and prove its convergence in real Hilbert spaces. We then use this framework to derive primal-dual splitting algorithms for solving various classes of monotone inclusions in…