相关论文: Douglas-Rachford splitting algorithm for projected…

This paper investigates the distributed fixed point finding problem for a global operator over a directed and unbalanced multi-agent network, where the global operator is quasinonexpansive and only partially accessible to each individual…

The Peaceman--Rachford scheme is a commonly used splitting method for discretizing semilinear evolution equations, where the vector fields are given by the sum of one linear and one nonlinear dissipative operator. Typical examples of such…

We propose a primal-dual backward reflected forward splitting method for solving structured primal-dual monotone inclusion in real Hilbert space. The algorithm allows to use the inexact computations of the Lipschitzian and cocoercive…

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…

This article analyses the simple projection method proposed by Izuchukwu et al. [8, Algorithm 3.2] for solving variational inequality problems by incorporating momentum terms. A new step size strategy is also introduced, in which the step…

Block-coordinate algorithms are recognized to furnish efficient iterative schemes for addressing large-scale problems, especially when the computation of full derivatives entails substantial memory requirements and computational efforts. In…

In this paper, we consider nonconvex decentralised optimisation and learning over a network of distributed agents. We develop an ADMM algorithm based on the Randomised Block Coordinate Douglas-Rachford splitting method which enables agents…

In this paper we describe a systematic procedure to analyze the convergence of degenerate preconditioned proximal point algorithms. We establish weak convergence results under mild assumptions that can be easily employed in the context of…

This paper considers the relaxed Peaceman-Rachford (PR) splitting method for finding an approximate solution of a monotone inclusion whose underlying operator consists of the sum of two maximal strongly monotone operators. Using general…

We introduce and analyze an abstract algorithm that aims to find the projection onto a closed convex subset of a Hilbert space. When specialized to the fixed point set of a quasi nonexpansive mapping, the required sufficient condition…

In this paper, we propose a reflected forward-backward splitting algorithic framework for finding a zero of the sum of finitely many monotone op-erators, including maximally monotone operators, cocoercive operators, and monotone and…

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…

The Douglas-Rachford reflection method is a general purpose algorithm useful for solving the feasibility problem of finding a point in the intersection of finitely many sets. In this chapter we demonstrate that applied to a specific…

We address the problem of projecting a point onto a quadratic hypersurface, more specifically a central quadric. We show how this problem reduces to finding a given root of a scalar-valued nonlinear function. We completely characterize one…

The Douglas--Rachford (DR) and alternating direction method of multipliers (ADMM) are two proximal splitting algorithms designed to minimize the sum of two proper lower semi-continuous convex functions whose proximity operators are easy to…

A new result in convex analysis on the calculation of proximity operators in certain scaled norms is derived. We describe efficient implementations of the proximity calculation for a useful class of functions; the implementations exploit…

Problems of the numerical solution of the Cauchy problem for a first-order differential-operator equation are discussed. A fundamental feature of the problem under study is that the equation includes a fractional power of the self-adjoint…

We introduce the circumcenter mapping induced by a set of (usually nonexpansive) operators. One prominent example of a circumcenter mapping is the celebrated Douglas--Rachford splitting operator. Our study is motivated by the…

This work is devoted to establish the strong convergence results of an iterative algorithm generated by the shrinking projection method in Hilbert spaces. The proposed approximation sequence is used to find a common element in the set of…

The main challenge of nonconvex optimization is to find a global optimum, or at least to avoid ``bad'' local minima and meaningless stationary points. We study here the extent to which algorithms, as opposed to optimization models and…