Related papers: Finding Dantzig selectors with a proximity operato…
We consider a minimization problem of the form $P(\varphi, g, h):$ $$\min\left\{f(x):= \varphi(x) + g(x) - h(x) \colon x \in \mathbb{R}^n\right\},$$ where $\varphi$ is a differentiable function and $g,$ $h$ are convex functions, and…
In many problems involving generalized linear models, the covariates are subject to measurement error. When the number of covariates p exceeds the sample size n, regularized methods like the lasso or Dantzig selector are required. Several…
Progressive Hedging is a popular decomposition algorithm for solving multi-stage stochastic optimization problems. A computational bottleneck of this algorithm is that all scenario subproblems have to be solved at each iteration. In this…
We study the behavior of deterministic methods for solving inverse problems in imaging. These methods are commonly designed to achieve two goals: (1) attaining high perceptual quality, and (2) generating reconstructions that are consistent…
We propose and analyze an accelerated iterative dual diagonal descent algorithm for the solution of linear inverse problems with general regularization and data-fit functions. In particular, we develop an inertial approach of which we…
Optical imaging quality can be severely degraded by system and sample induced aberrations. Existing adaptive optics systems typically rely on iterative search algorithm to correct for aberrations and improve images. This study demonstrates…
Finding multiple solutions of non-convex optimization problems is a ubiquitous yet challenging task. Most past algorithms either apply single-solution optimization methods from multiple random initial guesses or search in the vicinity of…
We present iterative solvers to approximate the solution of numerical schemes for stochastic Stefan problems. After briefly talking about the convergence results, we tackle the question of efficient strategies for solving the nonlinear…
In this article, we introduce a finite element method designed for the robust computation of approximate signed distance functions to arbitrary boundaries in two and three dimensions. Our method employs a novel prediction-correction…
A second order accurate numerical scheme is proposed and implemented for the Landau-Lifshitz-Gilbert equation, which models magnetization dynamics in ferromagnetic materials, with large damping parameters. The main advantages of this method…
We establish linear convergence of relocated fixed-point iterations as introduced by Atenas et al. (2025) assuming the algorithmic operator satisfies a linear error bound. In particular, this framework applies to the setting where the…
As first-order optimization methods become the method of choice for solving large-scale optimization problems, optimization solvers based on first-order algorithms are being built. Such general-purpose solvers must robustly detect…
We introduce and analyze a fast iterative method based on sequential Bregman projections for nonlinear inverse problems in Banach spaces. The key idea, in contrast to the standard Landweber method, is to use multiple search directions per…
We present a proximal gradient method for solving convex multiobjective optimization problems, where each objective function is the sum of two convex functions, with one assumed to be continuously differentiable. The algorithm incorporates…
We present some new results on the dynamic regressor extension and mixing parameter estimators for linear regression models recently proposed in the literature. This technique has proven instrumental in the solution of several open problems…
This paper presents and investigates an inexact proximal gradient method for solving composite convex optimization problems characterized by an objective function composed of a sum of a full-domain differentiable convex function and a…
We present a dynamic programming algorithm for selecting a representative subset of size $k$ from a given set with $n$ points such that the Riesz $s$-energy is near minimized. While NP-hard in general dimensions, the one-dimensional case…
We propose a method for variable selection in discriminant analysis with mixed categorical and continuous variables. This method is based on a criterion that permits to reduce the variable selection problem to a problem of estimating…
Gradient boosting is a prediction method that iteratively combines weak learners to produce a complex and accurate model. From an optimization point of view, the learning procedure of gradient boosting mimics a gradient descent on a…
We derive a posteriori error estimators for an optimal control problem governed by a convection-reaction-diffusion equation; control constraints are also considered. We consider a family of low-order stabilized finite element methods to…