Fair Primal Dual Splitting Method for Image Inverse Problems

Image inverse problems have numerous applications, including image processing, super-resolution, and computer vision, which are important areas in image science. These application models can be seen as a three-function composite optimization problem solvable by a variety of primal dual-type methods. We propose a fair primal dual algorithmic framework that incorporates the smooth term not only into the primal subproblem but also into the dual subproblem. We unify the global convergence and establish the convergence rates of our proposed fair primal dual method. Experiments on image denoising and super-resolution reconstruction demonstrate the superiority of the proposed method over the current state-of-the-art.

Novel clustered federated learning based on local loss

This paper proposes LCFL, a novel clustering metric for evaluating clients' data distributions in federated learning. LCFL aligns with federated learning requirements, accurately assessing client-to-client variations in data distribution. It offers advantages over existing clustered federated learning methods, addressing privacy concerns, improving applicability to non-convex models, and providing more accurate classification results. LCFL does not require prior knowledge of clients' data distributions. We provide a rigorous mathematical analysis, demonstrating the correctness and feasibility of our framework. Numerical experiments with neural network instances highlight the superior performance of LCFL over baselines on several clustered federated learning benchmarks.

Non-convex Pose Graph Optimization in SLAM via Proximal Linearized Riemannian ADMM

Pose graph optimization (PGO) is a well-known technique for solving the pose-based simultaneous localization and mapping (SLAM) problem. In this paper, we represent the rotation and translation by a unit quaternion and a three-dimensional vector, and propose a new PGO model based on the von Mises-Fisher distribution. The constraints derived from the unit quaternions are spherical manifolds, and the projection onto the constraints can be calculated by normalization. Then a proximal linearized Riemannian alternating direction method of multipliers (PieADMM) is developed to solve the proposed model, which not only has low memory requirements, but also can update the poses in parallel. Furthermore, we establish the iteration complexity of $O(1/\epsilon^{2})$ of PieADMM for finding an $\epsilon$-stationary solution of our model. The efficiency of our proposed algorithm is demonstrated by numerical experiments on two synthetic and four 3D SLAM benchmark datasets.

A Momentum Accelerated Algorithm for ReLU-based Nonlinear Matrix Decomposition

Recently, there has been a growing interest in the exploration of Nonlinear Matrix Decomposition (NMD) due to its close ties with neural networks. NMD aims to find a low-rank matrix from a sparse nonnegative matrix with a per-element nonlinear function. A typical choice is the Rectified Linear Unit (ReLU) activation function. To address over-fitting in the existing ReLU-based NMD model (ReLU-NMD), we propose a Tikhonov regularized ReLU-NMD model, referred to as ReLU-NMD-T. Subsequently, we introduce a momentum accelerated algorithm for handling the ReLU-NMD-T model. A distinctive feature, setting our work apart from most existing studies, is the incorporation of both positive and negative momentum parameters in our algorithm. Our numerical experiments on real-world datasets show the effectiveness of the proposed model and algorithm. Moreover, the code is available at https://github.com/nothing2wang/NMD-TM.

The neural network models with delays for solving absolute value equations

An inverse-free neural network model with mixed delays is proposed for solving the absolute value equation (AVE) $Ax -|x| - b =0$, which includes an inverse-free neural network model with discrete delay as a special case. By using the Lyapunov-Krasovskii theory and the linear matrix inequality (LMI) method, the developed neural network models are proved to be exponentially convergent to the solution of the AVE. Compared with the existing neural network models for solving the AVE, the proposed models feature the ability of solving a class of AVE with $\|A^{-1}\|>1$. Numerical simulations are given to show the effectiveness of the two delayed neural network models.