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Under mild assumptions stochastic gradient methods asymptotically achieve an optimal rate of convergence if the arithmetic mean of all iterates is returned as an approximate optimal solution. However, in the absence of stochastic noise, the…

Optimization and Control · Mathematics 2022-10-06 Melinda Hagedorn , Florian Jarre

This paper considers the problem of unconstrained minimization of smooth convex functions having Lipschitz continuous gradients with known Lipschitz constant. We recently proposed an optimized gradient method (OGM) for this problem and…

Optimization and Control · Mathematics 2019-06-14 Donghwan Kim , Jeffrey A. Fessler

In this paper, we consider constrained optimization problems with convex, smooth objective and constraints. We propose a new stochastic gradient algorithm, called the Stochastic Moving Ball Approximation (SMBA) method, to solve this class…

Optimization and Control · Mathematics 2024-12-03 Nitesh Kumar Singh , Ion Necoara

Ill-posed linear inverse problems appear in many scientific setups, and are typically addressed by solving optimization problems, which are composed of data fidelity and prior terms. Recently, several works have considered a back-projection…

Optimization and Control · Mathematics 2021-08-10 Tom Tirer , Raja Giryes

Sketched gradient algorithms have been recently introduced for efficiently solving the large-scale constrained Least-squares regressions. In this paper we provide novel convergence analysis for the basic method {\it Gradient Projection…

Optimization and Control · Mathematics 2017-06-05 Junqi Tang , Mohammad Golbabaee , Mike Davies

We develop multi-step gradient methods for network-constrained optimization of strongly convex functions with Lipschitz-continuous gradients. Given the topology of the underlying network and bounds on the Hessian of the objective function,…

Optimization and Control · Mathematics 2015-06-12 Euhanna Ghadimi , Iman Shames , Mikael Johansson

This work focuses on convergence analysis of the projected gradient method for solving constrained convex minimization problem in Hilbert spaces. We show that the sequence of points generated by the method employing the Armijo linesearch…

Optimization and Control · Mathematics 2015-08-10 Jose Yunier Bello Cruz , Welington de Oliveira

Stochastic optimization algorithms with variance reduction have proven successful for minimizing large finite sums of functions. Unfortunately, these techniques are unable to deal with stochastic perturbations of input data, induced for…

Machine Learning · Statistics 2017-11-16 Alberto Bietti , Julien Mairal

A scaled conjugate gradient method that accelerates existing adaptive methods utilizing stochastic gradients is proposed for solving nonconvex optimization problems with deep neural networks. It is shown theoretically that, whether with…

Machine Learning · Computer Science 2024-12-17 Naoki Sato , Koshiro Izumi , Hideaki Iiduka

This paper presents a novel stochastic gradient descent algorithm for constrained optimization. The proposed algorithm randomly samples constraints and components of the finite sum objective function and relies on a relaxed logarithmic…

Optimization and Control · Mathematics 2025-05-13 Naum Dimitrieski , Jing Cao , Christian Ebenbauer

In this paper, we combine the positive aspects of the Gradient Sampling (GS) and bundle methods, as the most efficient methods in nonsmooth optimization, to develop a robust method for solving unconstrained nonsmooth convex optimization…

Optimization and Control · Mathematics 2019-11-26 M. Maleknia , M. Shamsi

Large-scale constrained optimization problems are at the core of many tasks in control, signal processing, and machine learning. Notably, problems with functional constraints arise when, beyond a performance{\nobreakdash-}centric goal…

Optimization and Control · Mathematics 2025-05-15 Antesh Upadhyay , Sang Bin Moon , Abolfazl Hashemi

Much recent research effort has been directed to the development of efficient algorithms for solving minimax problems with theoretical convergence guarantees due to the relevance of these problems to a few emergent applications. In this…

Optimization and Control · Mathematics 2023-01-18 Zi Xu , Huiling Zhang , Yang Xu , Guanghui Lan

Classical stochastic gradient methods are well suited for minimizing expected-value objective functions. However, they do not apply to the minimization of a nonlinear function involving expected values or a composition of two expected-value…

Machine Learning · Statistics 2014-11-17 Mengdi Wang , Ethan X. Fang , Han Liu

There has been a growing effort in studying the distributed optimization problem over a network. The objective is to optimize a global function formed by a sum of local functions, using only local computation and communication. Literature…

Optimization and Control · Mathematics 2017-05-02 Guannan Qu , Na Li

In the past several years, the last-iterate convergence of the Stochastic Gradient Descent (SGD) algorithm has triggered people's interest due to its good performance in practice but lack of theoretical understanding. For Lipschitz convex…

Machine Learning · Computer Science 2026-03-20 Zijian Liu , Zhengyuan Zhou

Stochastic-gradient-based optimization has been a core enabling methodology in applications to large-scale problems in machine learning and related areas. Despite the progress, the gap between theory and practice remains significant, with…

Optimization and Control · Mathematics 2021-01-01 Lihua Lei , Michael I. Jordan

A generalized conditional gradient method for minimizing the sum of two convex functions, one of them differentiable, is presented. This iterative method relies on two main ingredients: First, the minimization of a partially linearized…

Optimization and Control · Mathematics 2021-10-01 Karl Kunisch , Daniel Walter

This paper is concerned with some new projection methods for solving variational inequality problems with monotone and Lipschitz-continuous mapping in Hilbert space. First, we propose the projected reflected gradient algorithm with a…

Optimization and Control · Mathematics 2018-03-26 Yu. Malitsky

It is often observed that stochastic gradient descent (SGD) and its variants implicitly select a solution with good generalization performance; such implicit bias is often characterized in terms of the sharpness of the minima. Kleinberg et…

Machine Learning · Statistics 2024-05-28 Atsushi Nitanda , Ryuhei Kikuchi , Shugo Maeda , Denny Wu