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The goal of the paper is development of an optimization method with the superlinear convergence rate for a nonsmooth convex function. For optimization an approximation is used that is similar to the Steklov integral averaging. The…

Optimization and Control · Mathematics 2023-08-03 I. M. Prudnikov

Stochastic model-based methods have received increasing attention lately due to their appealing robustness to the stepsize selection and provable efficiency guarantee. We make two important extensions for improving model-based methods on…

Optimization and Control · Mathematics 2021-11-16 Qi Deng , Wenzhi Gao

In this paper, we discuss the problem of minimizing the sum of two convex functions: a smooth function plus a non-smooth function. Further, the smooth part can be expressed by the average of a large number of smooth component functions, and…

Machine Learning · Computer Science 2016-11-17 Luo Luo , Zihao Chen , Zhihua Zhang , Wu-Jun Li

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

We present a stochastic optimization method that uses a fourth-order regularized model to find local minima of smooth and potentially non-convex objective functions with a finite-sum structure. This algorithm uses sub-sampled derivatives…

Optimization and Control · Mathematics 2023-07-18 Aurelien Lucchi , Jonas Kohler

In this work, we present a globalized stochastic semismooth Newton method for solving stochastic optimization problems involving smooth nonconvex and nonsmooth convex terms in the objective function. We assume that only noisy gradient and…

Optimization and Control · Mathematics 2018-03-12 Andre Milzarek , Xiantao Xiao , Shicong Cen , Zaiwen Wen , Michael Ulbrich

The stochastic proximal point (SPP) methods have gained recent attention for stochastic optimization, with strong convergence guarantees and superior robustness to the classic stochastic gradient descent (SGD) methods showcased at little to…

Machine Learning · Statistics 2023-01-10 Xiao-Tong Yuan , Ping Li

We analyze convergence rates of stochastic optimization procedures for non-smooth convex optimization problems. By combining randomized smoothing techniques with accelerated gradient methods, we obtain convergence rates of stochastic…

Optimization and Control · Mathematics 2012-04-10 John C. Duchi , Peter L. Bartlett , Martin J. Wainwright

We propose a new method for unconstrained optimization of a smooth and strongly convex function, which attains the optimal rate of convergence of Nesterov's accelerated gradient descent. The new algorithm has a simple geometric…

Optimization and Control · Mathematics 2015-06-30 Sébastien Bubeck , Yin Tat Lee , Mohit Singh

In this paper, we investigate the non-asymptotic stationary convergence behavior of Stochastic Mirror Descent (SMD) for nonconvex optimization. We focus on a general class of nonconvex nonsmooth stochastic optimization problems, in which…

Optimization and Control · Mathematics 2018-06-14 Siqi Zhang , Niao He

Composite convex optimization problems which include both a nonsmooth term and a low-rank promoting term have important applications in machine learning and signal processing, such as when one wishes to recover an unknown matrix that is…

Machine Learning · Computer Science 2018-09-28 Dan Garber , Atara Kaplan

We study constrained nested stochastic optimization problems in which the objective function is a composition of two smooth functions whose exact values and derivatives are not available. We propose a single time-scale stochastic…

Optimization and Control · Mathematics 2019-09-09 Saeed Ghadimi , Andrzej Ruszczyński , Mengdi Wang

Stochastic gradient methods are scalable for solving large-scale optimization problems that involve empirical expectations of loss functions. Existing results mainly apply to optimization problems where the objectives are one- or two-level…

Optimization and Control · Mathematics 2018-01-15 Shuoguang Yang , Mengdi Wang , Ethan X. Fang

We consider minimization of stochastic functionals that are compositions of a (potentially) non-smooth convex function $h$ and smooth function $c$ and, more generally, stochastic weakly-convex functionals. We develop a family of stochastic…

Optimization and Control · Mathematics 2018-09-25 John Duchi , Feng Ruan

We propose a framework to use Nesterov's accelerated method for constrained convex optimization problems. Our approach consists of first reformulating the original problem as an unconstrained optimization problem using a continuously…

Optimization and Control · Mathematics 2021-03-12 Priyank Srivastava , Jorge Cortes

This paper focuses on stochastic proximal gradient methods for optimizing a smooth non-convex loss function with a non-smooth non-convex regularizer and convex constraints. To the best of our knowledge we present the first non-asymptotic…

Optimization and Control · Mathematics 2019-05-27 Michael R. Metel , Akiko Takeda

In this paper we consider finite sum composite convex optimization problems with many functional constraints. The objective function is expressed as a finite sum of two terms, one of which admits easy computation of (sub)gradients while the…

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

In this paper, a novel stochastic extra-step quasi-Newton method is developed to solve a class of nonsmooth nonconvex composite optimization problems. We assume that the gradient of the smooth part of the objective function can only be…

Optimization and Control · Mathematics 2019-10-22 Minghan Yang , Andre Milzarek , Zaiwen Wen , Tong Zhang

This paper is devoted to some approaches for convex min-min problems with smoothness and strong convexity in only one of the two variable groups. It is shown that the proposed approaches, based on Vaidya's cutting plane method and…

Optimization and Control · Mathematics 2021-02-02 Egor Gladin , Mohammad Alkousa , Alexander Gasnikov

We propose mS2GD: a method incorporating a mini-batching scheme for improving the theoretical complexity and practical performance of semi-stochastic gradient descent (S2GD). We consider the problem of minimizing a strongly convex function…

Machine Learning · Computer Science 2016-04-20 Jakub Konečný , Jie Liu , Peter Richtárik , Martin Takáč