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We adapt the quasi-monotone method from [2] for composite convex minimization in the stochastic setting. For the proposed numerical scheme we derive the optimal convergence rate in terms of the last iterate, rather than on average as it is…

Optimization and Control · Mathematics 2021-07-09 Vyacheslav Kungurtsev , Vladimir Shikhman

Quasi-Newton methods are widely used for solving convex optimization problems due to their ease of implementation, practical efficiency, and strong local convergence guarantees. However, their global convergence is typically established…

Optimization and Control · Mathematics 2025-08-28 Artem Agafonov , Vladislav Ryspayev , Samuel Horváth , Alexander Gasnikov , Martin Takáč , Slavomir Hanzely

We consider the problem of how to learn a step-size policy for the Limited-Memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm. This is a limited computational memory quasi-Newton method widely used for deterministic unconstrained…

Machine Learning · Computer Science 2021-02-11 Lucas N. Egidio , Anders Hansson , Bo Wahlberg

In this article, we propose a quasi-Newton method for unconstrained set optimization problems to find its weakly minimal solutions with respect to lower set-less ordering. The set-valued objective mapping under consideration is given by a…

Optimization and Control · Mathematics 2025-01-10 Debdas Ghosh , Anshika , Jen-Chih Yao , Xiaopeng Zhao

In this manuscript, we propose a general proximal quasi-Newton method tailored for nonconvex and nonsmooth optimization problems, where we do not require the sequence of the variable metric (or Hessian approximation) to be uniformly bounded…

Optimization and Control · Mathematics 2025-07-28 Xiaoxi Jia

We propose a continuous-time second-order optimization algorithm for solving unconstrained convex optimization problems with bounded Hessian. We show that this alternative algorithm has a comparable convergence rate to that of the…

Optimization and Control · Mathematics 2021-05-21 Hossein Moradian , Solmaz S. Kia

In this paper, we propose a distributed second- order method for reinforcement learning. Our approach is the fastest in literature so-far as it outperforms state-of-the-art methods, including ADMM, by significant margins. We achieve this by…

Optimization and Control · Mathematics 2016-08-08 Rasul Tutunov , Haitham Bou-Ammar , Ali Jadbabaie

In this paper, we propose a new randomized second-order optimization algorithm---Stochastic Subspace Cubic Newton (SSCN)---for minimizing a high dimensional convex function $f$. Our method can be seen both as a {\em stochastic} extension of…

Optimization and Control · Mathematics 2020-02-25 Filip Hanzely , Nikita Doikov , Peter Richtárik , Yurii Nesterov

Recently, sophisticated deep learning-based approaches have been developed for generating efficient initial guesses to accelerate the convergence of density functional theory (DFT) calculations. While the actual initial guesses are often…

Chemical Physics · Physics 2026-03-24 Zhe Liu , Yuyan Ni , Zhichen Pu , Qiming Sun , Siyuan Liu , Wen Yan

We introduce a framework for quasi-Newton forward--backward splitting algorithms (proximal quasi-Newton methods) with a metric induced by diagonal $\pm$ rank-$r$ symmetric positive definite matrices. This special type of metric allows for a…

Optimization and Control · Mathematics 2018-11-27 Stephen Becker , Jalal Fadili , Peter Ochs

Newton's method may exhibit slower convergence than vanilla Gradient Descent in its initial phase on strongly convex problems. Classical Newton-type multilevel methods mitigate this but, like Gradient Descent, achieve only linear…

Optimization and Control · Mathematics 2026-02-25 Nick Tsipinakis , Panos Parpas , Matthias Voigt

Newton's method may exhibit slower convergence than vanilla Gradient Descent in its initial phase on strongly convex problems. Classical Newton-type multilevel methods mitigate this but, like Gradient Descent, achieve only linear…

Optimization and Control · Mathematics 2026-03-05 Nick Tsipinakis , Panagiotis Tigkas , Panos Parpas

In [19], a general, inexact, efficient proximal quasi-Newton algorithm for composite optimization problems has been proposed and a sublinear global convergence rate has been established. In this paper, we analyze the convergence properties…

Numerical Analysis · Computer Science 2017-10-18 Hiva Ghanbari , Katya Scheinberg

In this thesis, we disentangle the generalized Gauss-Newton and approximate inference for Bayesian deep learning. The generalized Gauss-Newton method is an optimization method that is used in several popular Bayesian deep learning…

Machine Learning · Statistics 2020-07-24 Alexander Immer

Inspired by the recent work FedNL (Safaryan et al, FedNL: Making Newton-Type Methods Applicable to Federated Learning), we propose a new communication efficient second-order framework for Federated learning, namely FLECS. The proposed…

Optimization and Control · Mathematics 2022-06-07 Artem Agafonov , Dmitry Kamzolov , Rachael Tappenden , Alexander Gasnikov , Martin Takáč

We consider distributed optimization problems where forming the Hessian is computationally challenging and communication is a significant bottleneck. We develop unbiased parameter averaging methods for randomized second order optimization…

Machine Learning · Statistics 2020-02-18 Burak Bartan , Mert Pilanci

We formulate natural gradient variational inference (VI), expectation propagation (EP), and posterior linearisation (PL) as extensions of Newton's method for optimising the parameters of a Bayesian posterior distribution. This viewpoint…

Machine Learning · Statistics 2022-12-07 William J. Wilkinson , Simo Särkkä , Arno Solin

In this paper, we propose new methods to efficiently solve convex optimization problems encountered in sparse estimation, which include a new quasi-Newton method that avoids computing the Hessian matrix and improves efficiency, and we prove…

Optimization and Control · Mathematics 2023-09-06 Ryosuke Shimmura , Joe Suzuki

We propose an L-BFGS optimization algorithm on Riemannian manifolds using minibatched stochastic variance reduction techniques for fast convergence with constant step sizes, without resorting to linesearch methods designed to satisfy Wolfe…

Optimization and Control · Mathematics 2017-05-23 Anirban Roychowdhury

This paper proposes a novel class of block quasi-Newton methods for convex optimization which we call symmetric rank-$k$ (SR-$k$) methods. Each iteration of SR-$k$ incorporates the curvature information with~$k$ Hessian-vector products…

Optimization and Control · Mathematics 2024-07-25 Chengchang Liu , Cheng Chen , Luo Luo