相关论文: A new ADMM algorithm for the Euclidean median and …

Decentralized optimization algorithms are important in different contexts, such as distributed optimal power flow or distributed model predictive control, as they avoid central coordination and enable decomposition of large-scale problems.…

Recently, minimax optimization received renewed focus due to modern applications in machine learning, robust optimization, and reinforcement learning. The scale of these applications naturally leads to the use of first-order methods.…

In this paper we study the computation of the nonparametric maximum likelihood estimator (NPMLE) in multivariate mixture models. Our first approach discretizes this infinite dimensional convex optimization problem by fixing the support…

We study connections between Dykstra's algorithm for projecting onto an intersection of convex sets, the augmented Lagrangian method of multipliers or ADMM, and block coordinate descent. We prove that coordinate descent for a regularized…

Latent Euclidean embedding models a given network by representing each node in a Euclidean space, where the probability of two nodes sharing an edge is a function of the distances between the nodes. This implies that for two nodes to share…

We investigate the purely spatial Lagrangian coordinate transformation from the Lagrangian to the basic Eulerian frame. We demonstrate three techniques for extracting the relativistic displacement field from a given solution in the…

One of the most fundamental concepts in statistics is the concept of sample mean. Properties of the sample mean that are well-defined in Euclidean spaces become unwieldy or even unclear in graph spaces. Open problems related to the sample…

Estimators derived from an EM algorithm are not robust since they are based on the maximization of the likelihood function. We propose a proximal-point algorithm based on the EM algorithm which aim to minimize a divergence criterion.…

The augmented Lagrangiam method (ALM), widely used in quantum chemistry constrained optimization problems, is applied in the context of the nuclear Density Functional Theory (DFT) in the self-consistent constrained Skyrme…

Distributed stochastic optimization algorithms can simultaneously process large-scale datasets, significantly accelerating model training. However, their effectiveness is often hindered by the sparsity of distributed networks and data…

This paper presents a new linear hyperspectral unmixing method of the minimum volume class, termed \emph{simplex identification via split augmented Lagrangian} (SISAL). Following Craig's seminal ideas, hyperspectral linear unmixing amounts…

We will propose a new algorithm for finding critical points of cost functions defined on a differential manifold. We will lift the initial cost function to a manifold that can be embedded in a Riemannian manifold (Euclidean space) and will…

The alternating direction method of multipliers (ADMM) algorithm is a powerful and flexible tool for complex optimization problems of the form $\min\{f(x)+g(y) : Ax+By=c\}$. ADMM exhibits robust empirical performance across a range of…

The EM algorithm is a widely used methodology for penalized likelihood estimation. Provable monotonicity and convergence are the hallmarks of the EM algorithm and these properties are well established for smooth likelihood and smooth…

The approximation of invariant measures for nonlinear ergodic stochastic differential equations (SDEs) is a central problem in scientific computing, with important applications in stochastic sampling, physics, and ecology. We first propose…

The Anderson Mixing (AM) method is a popular approach for accelerating fixed-point iterations by leveraging historical information from previous steps. In this paper, we introduce the Riemannian Anderson Mixing (RAM) method, an extension of…

Low-dimensional structure in real-world data plays an important role in the success of generative models, which motivates diffusion models defined on intrinsic data manifolds. Such models are driven by stochastic differential equations…

In this paper, we propose a unified framework of inexact stochastic Alternating Direction Method of Multipliers (ADMM) for solving nonconvex problems subject to linear constraints, whose objective comprises an average of finite-sum smooth…

This study develops an algorithm for distributed computing of linear programming problems of huge-scales. Global consensus with single common variable, multiblocks, and augmented Lagrangian are adopted. The consensus is used to partition…

Based on a nonlocal Laplacian operator, a novel edge detection method of the grayscale image is proposed in this paper. This operator utilizes the information of neighbor pixels for a given pixel to obtain effective and delicate edge…