Related papers: Regularized Extragradient Methods for Solving Equi…
In this paper, we propose two regularized proximal quasi-Newton methods with symmetric rank-1 update of the metric (SR1 quasi-Newton) to solve non-smooth convex additive composite problems. Both algorithms avoid using line search or other…
We present a framework for smooth optimization of explicitly regularized objectives for (structured) sparsity. These non-smooth and possibly non-convex problems typically rely on solvers tailored to specific models and regularizers. In…
We discuss recent advances in the regularity problem of a variety of fluid equations and systems. The purpose is to illustrate the advantage of harmonic analysis techniques in obtaining sharper conditional regularity results when compared…
We consider regular polynomial interpolation algorithms on recursively defined sets of interpolation points which approximate global solutions of arbitrary well-posed systems of linear partial differential equations. Convergence of the…
Dimensional regularization of Euclidean momentum space integrals is a highly successful technique in renormalization of quantum field theories. While it yields a straightforward algorithmic method, with which to evaluate diagrams beyond…
A multiscale numerical method is proposed for the solution of semi-linear elliptic stochastic partial differential equations with localized uncertainties and non-linearities, the uncertainties being modeled by a set of random parameters. It…
We introduce a generalized finite difference method for solving a large range of fully nonlinear elliptic partial differential equations in three dimensions. Methods are based on Cartesian grids, augmented by additional points carefully…
Successive quadratic approximations, or second-order proximal methods, are useful for minimizing functions that are a sum of a smooth part and a convex, possibly nonsmooth part that promotes regularization. Most analyses of iteration…
In this paper, we propose and analyze a fast two-point gradient algorithm for solving nonlinear ill-posed problems, which is based on the sequential subspace optimization method. A complete convergence analysis is provided under the…
This paper studies the iteration-complexity of new regularized hybrid proximal extragradient (HPE)-type methods for solving monotone inclusion problems (MIPs). The new (regularized HPE-type) methods essentially consist of instances of the…
We study how to solve semidefinite programming relaxations for large scale polynomial optimization. When interior-point methods are used, typically only small or moderately large problems could be solved. This paper studies regularization…
We introduce an algorithm to solve linear inverse problems regularized with the total (gradient) variation in a gridless manner. Contrary to most existing methods, that produce an approximate solution which is piecewise constant on a fixed…
We propose and analyze a two-level method for mimetic finite difference approximations of second order elliptic boundary value problems. We prove that the two-level algorithm is uniformly convergent, i.e., the number of iterations needed to…
This Note aims at presenting a simple and efficient procedure to derive the structure of high-order corrector estimates for the homogenization limit applied to a semi-linear elliptic equation posed in perforated domains. Our working…
We propose an extremely versatile approach to address a large family of matrix nearness problems, possibly with additional linear constraints. Our method is based on splitting a matrix nearness problem into two nested optimization problems,…
This paper considers the problems of solving monotone variational inequalities with H\"older continuous Jacobians. By employing the knowledge of H\"older parameter $\nu$, we propose the $\nu$-regularized extra-Newton method within at most…
In this paper, we propose two novel parallel hybrid methods for finding a common element of the set of solutions of a finite family of generalized equilibrium problems for monotone bifunctions $\left\{f_i\right\}_{i=1}^N$ and $\alpha$ -…
We consider scalar equilibrium problems governed by a bifunction in a finite-dimensional framework. By using classical arguments in Convex Analysis, we show that under suitable generalized convexity assumptions imposed on the bifunction,…
This paper is concerned with $\ell_q\,(0<q<1)$-norm regularized minimization problems with a twice continuously differentiable loss function. For this class of nonconvex and nonsmooth composite problems, many algorithms have been proposed…
In this paper, we focus on nonlinear infinite-norm minimization problems that have many applications, especially in computer science and operations research. We set a reliable Lagrangian dual aproach for solving this kind of problems in…