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In this paper, a new variant of accelerated gradient descent is proposed. The pro-posed method does not require any information about the objective function, usesexact line search for the practical accelerations of convergence, converges…

Optimization and Control · Mathematics 2019-05-14 Yurii Nesterov , Alexander Gasnikov , Sergey Guminov , Pavel Dvurechensky

In this paper, we propose a method that has foundations in the line search sequential quadratic programming paradigm for solving general nonlinear equality constrained optimization problems. The method employs a carefully designed modified…

Optimization and Control · Mathematics 2024-07-29 Albert S. Berahas , Raghu Bollapragada , Jiahao Shi

The classical line search for learning rate (LR) tuning in the stochastic gradient descent (SGD) algorithm can tame the convergence slowdown due to data-sampling noise. In a federated setting, wherein the client heterogeneity introduces a…

Machine Learning · Computer Science 2025-10-28 Geetika , Somya Tyagi , Bapi Chatterjee

In deterministic optimization, line searches are a standard tool ensuring stability and efficiency. Where only stochastic gradients are available, no direct equivalent has so far been formulated, because uncertain gradients do not allow for…

Machine Learning · Computer Science 2017-07-03 Maren Mahsereci , Philipp Hennig

In deterministic optimization, line searches are a standard tool ensuring stability and efficiency. Where only stochastic gradients are available, no direct equivalent has so far been formulated, because uncertain gradients do not allow for…

Machine Learning · Computer Science 2016-01-19 Maren Mahsereci , Philipp Hennig

The Conditional Gradient Method is generalized to a class of non-smooth non-convex optimization problems with many applications in machine learning. The proposed algorithm iterates by minimizing so-called model functions over the constraint…

Optimization and Control · Mathematics 2019-01-25 Yura Malitsky , Peter Ochs

In this paper, we consider a class of possibly nonconvex, nonsmooth and non-Lipschitz optimization problems arising in many contemporary applications such as machine learning, variable selection and image processing. To solve this class of…

Optimization and Control · Mathematics 2021-09-29 Lei Yang

Linear optimization is many times algorithmically simpler than non-linear convex optimization. Linear optimization over matroid polytopes, matching polytopes and path polytopes are example of problems for which we have simple and efficient…

Machine Learning · Computer Science 2015-08-17 Dan Garber , Elad Hazan

The existing machine learning algorithms for minimizing the convex function over a closed convex set suffer from slow convergence because their learning rates must be determined before running them. This paper proposes two machine learning…

Optimization and Control · Mathematics 2019-09-02 Kazuhiro Hishinuma , Hideaki Iiduka

We analyse the convergence of the proximal gradient algorithm for convex composite problems in the presence of gradient and proximal computational inaccuracies. We derive new tighter deterministic and probabilistic bounds that we use to…

Optimization and Control · Mathematics 2022-03-07 Anis Hamadouche , Yun Wu , Andrew M. Wallace , Joao F. C. Mota

We devise a new accelerated gradient-based estimating sequence technique for solving large-scale optimization problems with composite structure. More specifically, we introduce a new class of estimating functions, which are obtained by…

Optimization and Control · Mathematics 2021-11-15 Endrit Dosti , Sergiy A. Vorobyov , Themistoklis Charalambous

In this work, we propose two derivative-free methods to address the problem of large-scale nonlinear equations with convex constraints. These algorithms satisfy the sufficient descent condition. The search directions can be considered…

Numerical Analysis · Mathematics 2025-11-17 Kabenge Hamiss , Mohammed M. Alshahrani , Mujahid N. Syed

Backtracking line-search is an old yet powerful strategy for finding a better step sizes to be used in proximal gradient algorithms. The main principle is to locally find a simple convex upper bound of the objective function, which in turn…

Optimization and Control · Mathematics 2019-11-06 Mahesh Chandra Mukkamala , Peter Ochs , Thomas Pock , Shoham Sabach

We propose a variant of the approximate Bregman proximal gradient (ABPG) algorithm for minimizing the sum of a smooth nonconvex function and a nonsmooth convex function. ABPG is known to converge globally to a stationary point even when the…

Optimization and Control · Mathematics 2026-03-23 Kiwamu Fujiki , Shota Takahashi , Akiko Takeda

We consider descent methods for solving non-finite valued nonsmooth convex-composite optimization problems that employ Gauss-Newton subproblems to determine the iteration update. Specifically, we establish the global convergence properties…

Optimization and Control · Mathematics 2019-09-11 James V. Burke , Abraham Engle

We propose a novel linesearch variant of the trust region normal map-based semismooth Newton method developed in [Ouyang and Milzarek, Math. Program. 212(1-2), 389--435 (2025)] for solving a class of nonsmooth, nonconvex composite-type…

Optimization and Control · Mathematics 2026-02-16 Hanfeng Zeng , Wenqing Ouyang , Andre Milzarek

There has been much recent interest in finding unconstrained local minima of smooth functions, due in part of the prevalence of such problems in machine learning and robust statistics. A particular focus is algorithms with good complexity…

Optimization and Control · Mathematics 2017-12-12 Clément W. Royer , Stephen J. Wright

Accelerating the convergence of second-order optimization, particularly Newton-type methods, remains a pivotal challenge in algorithmic research. In this paper, we extend previous work on the \textbf{Quadratic Gradient (QG)} and rigorously…

Optimization and Control · Mathematics 2026-04-01 John Chiang

This paper deals with the minimization of large sum of convex functions by Inexact Newton (IN) methods employing subsampled functions, gradients and Hessian approximations. The Conjugate Gradient method is used to compute the inexact Newton…

Numerical Analysis · Mathematics 2018-11-15 Stefania Bellavia , Natasa Krejic , Natasa Krklec Jerinkic

This paper explores variants of the subspace iteration algorithm for computing approximate invariant subspaces. The standard subspace iteration approach is revisited and new variants that exploit gradient-type techniques combined with a…

Numerical Analysis · Mathematics 2024-05-14 Foivos Alimisis , Yousef Saad , Bart Vandereycken