Concept

Modes of convergence

Related publications (20)

Full-F turbulent simulation in a linear plasma device using a gyro-moment approach

Simulations of plasma turbulence in a linear plasma device configuration are presented. These simulations are based on a simplified version of the gyrokinetic (GK) model proposed by Frei et al. [J. Plasma Phys. 86, 905860205 (2020)], where the full-F distr ...

Melville2024

Localization errors of the stochastic heat equation

David Jean-Michel Candil

In this thesis, we study the stochastic heat equation (SHE) on bounded domains and on the whole Euclidean space

\R^d.

We confirm the intuition that as the bounded domain increases to the whole space, both solutions become arbitrarily close to one another ...

EPFL2022

Decentralized Proximal Gradient Algorithms With Linear Convergence Rates

Ali H. Sayed, Kun Yuan, Sulaiman A S A E Alghunaim

This article studies a class of nonsmooth decentralized multiagent optimization problems where the agents aim at minimizing a sum of local strongly-convex smooth components plus a common nonsmooth term. We propose a general primal-dual algorithmic framewor ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2021

Variance-Reduced Stochastic Learning Under Random Reshuffling

Ali H. Sayed, Bicheng Ying, Kun Yuan

Several useful variance-reduced stochastic gradient algorithms, such as SVRG, SAGA, Finito, and SAG, have been proposed to minimize empirical risks with linear convergence properties to the exact minimizer. The existing convergence results assume uniform d ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2020

Hubbard-corrected density functional perturbation theory with ultrasoft pseudopotentials

Nicola Marzari, Iurii Timrov, Matteo Cococcioni, Andrea Floris

We present in full detail a newly developed formalism enabling density functional perturbation theory (DFPT) calculations from a DFT + U ground state. The implementation includes ultrasoft pseudopotentials and is valid for both insulating and metallic syst ...

AMER PHYSICAL SOC2020

A Linearly Convergent Proximal Gradient Algorithm for Decentralized Optimization

Ali H. Sayed, Kun Yuan, Sulaiman A S A E Alghunaim

Decentralized optimization is a powerful paradigm that finds applications in engineering and learning design. This work studies decentralized composite optimization problems with non-smooth regularization terms. Most existing gradient-based proximal decent ...

NEURAL INFORMATION PROCESSING SYSTEMS (NIPS)2019

Convergence Of Variance-Reduced Learning Under Random Reshuffling

Ali H. Sayed, Bicheng Ying, Kun Yuan

Several useful variance-reduced stochastic gradient algorithms, such as SVRG, SAGA, Finito, and SAG, have been proposed to minimize empirical risks with linear convergence properties to the exact minimizers. The existing convergence results assume uniform ...

IEEE2018

Convergence analysis of Padé approximations for Helmholtz frequency response problems

Fabio Nobile, Francesca Bonizzoni

The present work concerns the approximation of the solution map

S

associated to the parametric Helmholtz boundary value problem, i.e., the map which associates to each (real) wavenumber belonging to a given interval of interest the corresponding solution ...

2018

On the linear convergence of the stochastic gradient method with constant step-size

Volkan Cevher, Cong Bang Vu

The strong growth condition (SGC) is known to be a sufficient condition for linear convergence of the stochastic gradient method using a constant step-size γ (SGM-CS). In this paper, we provide a necessary condition, for the linear convergence of SGM-CS, t ...

2018

On Matching Pursuit and Coordinate Descent

Martin Jaggi, Sebastian Urban Stich, Sai Praneeth Reddy Karimireddy, Anant Raj

Two popular examples of first-order optimization methods over linear spaces are coordinate descent and matching pursuit algorithms, with their randomized variants. While the former targets the optimization by moving along coordinates, the latter considers ...

2018

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Localization errors of the stochastic heat equation

David Jean-Michel Candil

In this thesis, we study the stochastic heat equation (SHE) on bounded domains and on the whole Euclidean space

\R^d.

We confirm the intuition that as the bounded domain increases to the whole space, both solutions become arbitrarily close to one another ...

EPFL2022

Convergence analysis of Padé approximations for Helmholtz frequency response problems

Fabio Nobile, Francesca Bonizzoni

The present work concerns the approximation of the solution map

S

associated to the parametric Helmholtz boundary value problem, i.e., the map which associates to each (real) wavenumber belonging to a given interval of interest the corresponding solution ...

2018