相关论文: A Linearly Convergent Douglas-Rachford Splitting S…

Differentially private federated learning (DP-FL) enables clients to collaboratively train machine learning models while preserving the privacy of their local data. However, most existing DP-FL approaches assume that all clients share a…

We analyze a novel multi-level version of a recently introduced compressed sensing (CS) Petrov-Galerkin (PG) method from [H. Rauhut and Ch. Schwab: Compressive Sensing Petrov-Galerkin approximation of high-dimensional parametric operator…

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…

We present a class of reduced basis (RB) methods for the iterative solution of parametrized symmetric positive-definite (SPD) linear systems. The essential ingredients are a Galerkin projection of the underlying parametrized system onto a…

In this paper, we propose several graph-based extensions of the Douglas-Rachford splitting (DRS) method to solve monotone inclusion problems involving the sum of $N$ maximal monotone operators. Our construction is based on a two-layer…

Over the past years, operator splitting methods have become ubiquitous for non-smooth optimization owing to their simplicity and efficiency. In this paper, we consider the Forward--Douglas--Rachford splitting method (FDR) [10,40], and study…

The problem of finding a vector with the fewest nonzero elements that satisfies an underdetermined system of linear equations is an NP-complete problem that is typically solved numerically via convex heuristics or nicely-behaved nonconvex…

Motivated by nonconvex, inconsistent feasibility problems in imaging, the relaxed alternating averaged reflections algorithm, or relaxed Douglas-Rachford algorithm (DR$\lambda$), was first proposed over a decade ago. Convergence results for…

This paper proposes and develops new linesearch methods with inexact gradient information for finding stationary points of nonconvex continuously differentiable functions on finite-dimensional spaces. Some abstract convergence results for a…

Variational dimensionality reduction methods are widely used for their accuracy, generative capabilities, and robustness. We introduce a unifying framework that generalizes both such as traditional and state-of-the-art methods. The…

The information bottleneck (IB) approach to clustering takes a joint distribution $P\!\left(X,Y\right)$ and maps the data $X$ to cluster labels $T$ which retain maximal information about $Y$ (Tishby et al., 1999). This objective results in…

The growing public concerns on data privacy in face recognition can be greatly addressed by the federated learning (FL) paradigm. However, conventional FL methods perform poorly due to the uniqueness of the task: broadcasting class centers…

This paper introduces the distributed Halpern Peaceman--Rachford (dHPR) method, an efficient algorithm for solving distributed convex composite optimization problems with non-smooth objectives, which achieves a non-ergodic $O(1/k)$…

In the era of big data, the need to expand the amount of data through data sharing to improve model performance has become increasingly compelling. As a result, effective collaborative learning models need to be developed with respect to…

We investigate the problem of maximizing the sum-rate performance of a beyond-diagonal reconfigurable intelligent surface (BD-RIS)-aided multi-user (MU)-multiple-input single-output (MISO) system using fractional programming (FP)…

With the proliferation of smart devices having built-in sensors, Internet connectivity, and programmable computation capability in the era of Internet of things (IoT), tremendous data is being generated at the network edge. Federated…

Recently, several authors have shown local and global convergence rate results for Douglas-Rachford splitting under strong monotonicity, Lipschitz continuity, and cocoercivity assumptions. Most of these focus on the convex optimization…

Recent results in Compressive Sensing have shown that, under certain conditions, the solution to an underdetermined system of linear equations with sparsity-based regularization can be accurately recovered by solving convex relaxations of…

Differential privacy (DP) techniques can be applied to the federated learning model to protect data privacy against inference attacks to communication among the learning agents. The DP techniques, however, hinder achieving a greater…

The Douglas-Rachford method has been employed successfully to solve many kinds of non-convex feasibility problems. In particular, recent research has shown surprising stability for the method when it is applied to finding the intersections…