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Recent years have seen a growing interest in understanding acceleration methods through the lens of ordinary differential equations (ODEs). Despite the theoretical advancements, translating the rapid convergence observed in continuous-time…

Optimization and Control · Mathematics 2024-06-05 Zhonglin Xie , Wotao Yin , Zaiwen Wen

The stochastic momentum method is a commonly used acceleration technique for solving large-scale stochastic optimization problems in artificial neural networks. Current convergence results of stochastic momentum methods under non-convex…

Optimization and Control · Mathematics 2023-01-26 Dongpo Xu , Jinlan Liu , Yinghua Lu , Jun Kong , Danilo Mandic

The Iterative Hard Thresholding (IHT) algorithm has been considered extensively as an effective deterministic algorithm for solving sparse optimizations. The IHT algorithm benefits from the information of the batch (full) gradient at each…

Machine Learning · Computer Science 2022-09-30 Saeed Damadi , Jinglai Shen

We show that the herding procedure of Welling (2009) takes exactly the form of a standard convex optimization algorithm--namely a conditional gradient algorithm minimizing a quadratic moment discrepancy. This link enables us to invoke…

Machine Learning · Computer Science 2012-09-12 Francis Bach , Simon Lacoste-Julien , Guillaume Obozinski

Regularization of ill-posed linear inverse problems via $\ell_1$ penalization has been proposed for cases where the solution is known to be (almost) sparse. One way to obtain the minimizer of such an $\ell_1$ penalized functional is via an…

Numerical Analysis · Mathematics 2013-01-01 I. Daubechies , M. Fornasier , I. Loris

Convergence rates are established for an inexact accelerated alternating direction method of multipliers (I-ADMM) for general separable convex optimization with a linear constraint. Both ergodic and non-ergodic iterates are analyzed.…

Numerical Analysis · Mathematics 2021-07-20 William W. Hager , Hongchao Zhang

We extend the standard reinforcement learning framework to random time horizons. While the classical setting typically assumes finite and deterministic or infinite runtimes of trajectories, we argue that multiple real-world applications…

Machine Learning · Computer Science 2025-08-15 Enric Ribera Borrell , Lorenz Richter , Christof Schütte

The impact of different linearisation and iterative solution strategies for fully-coupled pressure-based algorithms for compressible flows at all speeds is studied, with the aim of elucidating their impact on the performance of the…

Computational Physics · Physics 2018-07-16 Fabian Denner

Higher-order tensor methods were recently proposed for minimizing smooth convex and nonconvex functions. Higher-order algorithms accelerate the convergence of the classical first-order methods thanks to the higher-order derivatives used in…

Optimization and Control · Mathematics 2024-01-11 Ion Necoara

Model training algorithms which observe a small portion of the training set in each computational step are ubiquitous in practical machine learning, and include both stochastic and online optimization methods. In the vast majority of cases,…

Machine Learning · Computer Science 2024-06-19 Alex Shtoff

The optimal learning rate for adaptive gradient methods applied to {\lambda}-strongly convex functions relies on the parameters {\lambda} and learning rate {\eta}. In this paper, we adapt a universal algorithm along the lines of Metagrad,…

Machine Learning · Computer Science 2023-07-18 Deepak Gouda , Hassan Naveed , Salil Kamath

Nonconvex and nonsmooth optimization problems are frequently encountered in much of statistics, business, science and engineering, but they are not yet widely recognized as a technology in the sense of scalability. A reason for this…

Optimization and Control · Mathematics 2018-01-19 Bo Jiang , Tianyi Lin , Shiqian Ma , Shuzhong Zhang

Stochastic optimization algorithms are widely used for large-scale data analysis due to their low per-iteration costs, but they often suffer from slow asymptotic convergence caused by inherent variance. Variance-reduced techniques have been…

Machine Learning · Statistics 2024-07-25 Derek Fox , Samuel Hernandez , Qianqian Tong

The purpose of this survey is to serve both as a gentle introduction and a coherent overview of state-of-the-art Frank--Wolfe algorithms, also called conditional gradient algorithms, for function minimization. These algorithms are…

The Primal-Dual hybrid gradient (PDHG) method is a powerful optimization scheme that breaks complex problems into simple sub-steps. Unfortunately, PDHG methods require the user to choose stepsize parameters, and the speed of convergence is…

Numerical Analysis · Mathematics 2015-03-25 Tom Goldstein , Min Li , Xiaoming Yuan , Ernie Esser , Richard Baraniuk

We build a theoretical framework for designing and understanding practical meta-learning methods that integrates sophisticated formalizations of task-similarity with the extensive literature on online convex optimization and sequential…

Machine Learning · Computer Science 2019-12-10 Mikhail Khodak , Maria-Florina Balcan , Ameet Talwalkar

This paper analyzes the convergence rates of the {\it Frank-Wolfe } method for solving convex constrained multiobjective optimization. We establish improved convergence rates under different assumptions on the objective function, the…

Optimization and Control · Mathematics 2024-06-11 Douglas S. Gonçalves , Max L. N. Gonçalves , Jefferson G. Melo

In this paper we analyse the Waveholtz method, a time-domain iterative method for solving the Helmholtz iteration, in the constant-coefficient case in all of $\mathbb{R}^d$. We show that the difference between a Waveholtz iterate and the…

Numerical Analysis · Mathematics 2025-10-20 Olof Runborg , Elliot Backman

Convergence detection of iterative stochastic optimization methods is of great practical interest. This paper considers stochastic gradient descent (SGD) with a constant learning rate and momentum. We show that there exists a transient…

Machine Learning · Computer Science 2020-08-28 Jerry Chee , Ping Li

Low-rank tensor recovery problems have been widely studied in many applications of signal processing and machine learning. Tucker decomposition is known as one of the most popular decompositions in the tensor framework. In recent years,…

Numerical Analysis · Mathematics 2020-07-17 Rachel Grotheer , Shuang Li , Anna Ma , Deanna Needell , Jing Qin