相关论文: Nonlinear Schwarz preconditioning for Quasi-Newton…
We present new convergence analyses for parallel subspace correction methods for unconstrained semicoercive and nearly semicoercive convex optimization problems, generalizing the theory of singular and nearly singular linear problems to a…
Recent studies incorporate Nesterov's accelerated gradient method for the acceleration of gradient based training. The Nesterov's Accelerated Quasi-Newton (NAQ) method has shown to drastically improve the convergence speed compared to the…
Despite the impressive numerical performance of the quasi-Newton and Anderson/nonlinear acceleration methods, their global convergence rates have remained elusive for over 50 years. This study addresses this long-standing issue by…
In this paper we introduce a new Schwarz framework and theory, based on the well-known idea of space decomposition, for nonsymmetric and indefinite linear systems arising from continuous and discontinuous Galerkin approximations of general…
The quasilinearization method (QLM) of solving nonlinear differential equations is applied to the quantum mechanics by casting the Schr\"{o}dinger equation in the nonlinear Riccati form. The method, whose mathematical basis in physics was…
Two-level domain decomposition preconditioners lead to fast convergence and scalability of iterative solvers. However, for highly heterogeneous problems, where the coefficient function is varying rapidly on several possibly non-separated…
A preconditioning strategy for the Powell-Hestenes-Rockafellar Augmented Lagrangian method (ALM) is presented. The scheme exploits the structure of the Augmented Lagrangian Hessian. It is a modular preconditioner consisting of two blocks.…
Variational models for image deblurring problems typically consist of a smooth term and a potentially non-smooth convex term. A common approach to solving these problems is using proximal gradient methods. To accelerate the convergence of…
We present and analyze a preconditioner of the additive Schwarz type for the mortar boundary element method. As a basic splitting, on each subdomain we separate the degrees of freedom related to its boundary from the inner degrees of…
Stochastic neighbor embedding (SNE) and related nonlinear manifold learning algorithms achieve high-quality low-dimensional representations of similarity data, but are notoriously slow to train. We propose a generic formulation of embedding…
Incompressible fluid flow problems appear frequently in different applications. The discretization of such problems may result in large and ill-conditioned systems of linear equations. We consider the case of the Stokes equations…
This work develops neural-network--based preconditioners to accelerate solution of the Wilson-Dirac normal equation in lattice quantum field theories. The approach is implemented for the two-flavor lattice Schwinger model near the critical…
Stochastic second-order methods achieve fast local convergence in strongly convex optimization by using noisy Hessian estimates to precondition the gradient. However, these methods typically reach superlinear convergence only when the…
Fast gradient-based optimization algorithms have become increasingly essential for the computationally efficient training of machine learning models. One technique is to multiply the gradient by a preconditioner matrix to produce a step,…
Update formulas for the Hessian approximations in quasi-Newton methods such as BFGS can be derived as analytical solutions to certain nearest-matrix problems. In this article, we propose a similar idea for deriving new limited memory…
Kernel methods are a popular class of nonlinear predictive models in machine learning. Scalable algorithms for learning kernel models need to be iterative in nature, but convergence can be slow due to poor conditioning. Spectral…
In this note we exploit polynomial preconditioners for the Conjugate Gradient method to solve large symmetric positive definite linear systems in a parallel environment. We put in connection a specialized Newton method to solve the matrix…
We introduce the primal-dual quasi-Newton (PD-QN) method as an approximated second order method for solving decentralized optimization problems. The PD-QN method performs quasi-Newton updates on both the primal and dual variables of the…
The problem of minimizing the sum of $n$ functions in $d$ dimensions is ubiquitous in machine learning and statistics. In many applications where the number of observations $n$ is large, it is necessary to use incremental or stochastic…
Least squares method is one of the simplest and most popular techniques applied in data fitting, imaging processing and high dimension data analysis. The classic methods like QR and SVD decomposition for solving least squares problems has a…