Related papers: A Bregman ADMM for Bethe variational problem

The Alternating Direction Method of Multipliers (ADMM) provides a natural way of solving inverse problems with multiple partial differential equations (PDE) forward models and nonsmooth regularization. ADMM allows splitting these…

This paper discusses basic results and recent developments on variational regularization methods, as developed for inverse problems. In a typical setup we review basic properties needed to obtain a convergent regularization scheme and…

An important problem that arises in many engineering applications is the boundary value problem for ordinary differential equations. There have been many computational methods proposed for dealing with this problem. The convergence of the…

We consider meshless approximation for solutions of boundary value problems (BVPs) of elliptic Partial Differential Equations (PDEs) via symmetric kernel collocation. We discuss the importance of the choice of the collocation points, in…

This study is concern with the numerical solution of the initial boundary value problem (IBVP) for the semilinear scale-invariant wave equation with damping and mass and power non-linearity. Numerical results of the aforementioned IBVP is…

We propose a fast algorithm for computing the GMM estimator in the BLP demand model (Berry, Levinsohn, and Pakes, 1995). Inspired by nested pseudo-likelihood methods for dynamic discrete choice models, our approach avoids repeatedly solving…

Owing to the recent advances in "Big Data" modeling and prediction tasks, variational Bayesian estimation has gained popularity due to their ability to provide exact solutions to approximate posteriors. One key technique for approximate…

In this paper we propose an adaptive scheme for the solution of time-dependent boundary value problems (BVPs). To solve numerically these problems, we consider the kernel-based method of lines that allows us to split the spatial and time…

Primal-dual splitting involving proximity operators in order to be able to find some approximation to the minimizer for a general form of Tikhonov type functional is in the focus of this work. This approximation is produced by a pair of…

In this paper, we study the finite-sum convex optimization problem focusing on the general convex case. Recently, the study of variance reduced (VR) methods and their accelerated variants has made exciting progress. However, the step size…

This article reports an algorithm for multi-agent distributed optimization problems with a common decision variable, local linear equality and inequality constraints and set constraints with convergence rate guarantees.…

We present an efficient alternating direction method of multipliers (ADMM) algorithm for segmenting a multivariate non-stationary time series with structural breaks into stationary regions. We draw from recent work where the series is…

Few methods in Bayesian non-parametric statistics/ machine learning have received as much attention as Bayesian Additive Regression Trees (BART). While BART is now routinely performed for prediction tasks, its theoretical properties began…

We consider the problem of minimizing the sum of two convex functions: one is differentiable and relatively smooth with respect to a reference convex function, and the other can be nondifferentiable but simple to optimize. We investigate a…

This work extends our previous study from S. Shrestha et al. (2024) by introducing a new abstract framework for Variational Multiscale (VMS) methods at the discrete level. We introduce the concept of what we define as the optimal projector…

To reduce complexity and achieve scalable performance in high-dimensional black-box settings, we propose a distributed method for nonconvex derivative-free optimization of continuous variables with an additively separable objective, subject…

We propose a distributed version of the Alternating Direction Method of Multipliers (ADMM) with linear updates for directed networks. We show that if the objective function of the minimization problem is smooth and strongly convex, our…

In this paper, we consider a class of nonconvex problems with linear constraints appearing frequently in the area of image processing. We solve this problem by the penalty method and propose the iteratively reweighted alternating…

This paper introduces the Bi-linear consensus Alternating Direction Method of Multipliers (Bi-cADMM), aimed at solving large-scale regularized Sparse Machine Learning (SML) problems defined over a network of computational nodes.…

We investigate convergence of alternating Bregman projections between non-convex sets and prove convergence to a point in the intersection, or to points realizing a gap between the two sets. The speed of convergence is generally sub-linear,…