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This paper studies non-smooth problems of convex stochastic optimization. Using the smoothing technique based on the replacement of the function value at the considered point by the averaged function value over a ball (in $l_1$-norm or…

Optimization and Control · Mathematics 2023-05-23 Aleksandr Lobanov , Belal Alashqar , Darina Dvinskikh , Alexander Gasnikov

Loss functions with non-isolated minima have emerged in several machine learning problems, creating a gap between theory and practice. In this paper, we formulate a new type of local convexity condition that is suitable to describe the…

Machine Learning · Computer Science 2022-05-31 Taehee Ko , Xiantao Li

We show that asymptotically, completely asynchronous stochastic gradient procedures achieve optimal (even to constant factors) convergence rates for the solution of convex optimization problems under nearly the same conditions required for…

Optimization and Control · Mathematics 2015-08-05 John C. Duchi , Sorathan Chaturapruek , Christopher Ré

We study a nonsmooth nonconvex optimization problem defined over nonconvex constraints, where the feasible set is given by the intersection of the closure of an open set and a smooth manifold. By endowing the open set with a Riemannian…

Optimization and Control · Mathematics 2025-07-28 Kuangyu Ding , Kim-Chuan Toh

Distributed optimization has gained significant attention in recent years, primarily fueled by the availability of a large amount of data and privacy-preserving requirements. This paper presents a fixed-time convergent optimization…

Systems and Control · Computer Science 2022-05-30 Kunal Garg , Mayank Baranwal

In this paper, we propose a new way to obtain optimal convergence rates for smooth stochastic (strong) convex optimization tasks. Our approach is based on results for optimization tasks where gradients have nonrandom noise. In contrast to…

Optimization and Control · Mathematics 2020-04-16 Darina Dvinskikh , Alexander Tyurin , Alexander Gasnikov , Sergey Omelchenko

Recently, several studies consider the stochastic optimization problem but in a heavy-tailed noise regime, i.e., the difference between the stochastic gradient and the true gradient is assumed to have a finite $p$-th moment (say being upper…

Optimization and Control · Mathematics 2023-05-23 Zijian Liu , Zhengyuan Zhou

In a separable real Hilbert space, we study the problem of minimizing a convex function with Lipschitz continuous gradient in the presence of noisy evaluations. To this end, we associate a stochastic Heavy Ball system, incorporating a…

Optimization and Control · Mathematics 2025-10-06 Radu Ioan Bot , Chiara Schindler

This paper proposes a stochastic gradient descent method with an adaptive Gaussian noise term for the global minimization of nearly convex functions, which are nonconvex and possess multiple strict local minimizers. The noise term,…

Optimization and Control · Mathematics 2025-08-05 Chenglong Bao , Liang Chen , Weizhi Shao

The usual approach to developing and analyzing first-order methods for smooth convex optimization assumes that the gradient of the objective function is uniformly smooth with some Lipschitz constant $L$. However, in many settings the…

Optimization and Control · Mathematics 2017-10-11 Haihao Lu , Robert M. Freund , Yurii Nesterov

In recent literature, a general two step procedure has been formulated for solving the problem of phase retrieval. First, a spectral technique is used to obtain a constant-error initial estimate, following which, the estimate is refined to…

Machine Learning · Statistics 2023-07-10 Yan Shuo Tan , Roman Vershynin

The stochastic gradient Langevin Dynamics is one of the most fundamental algorithms to solve sampling problems and non-convex optimization appearing in several machine learning applications. Especially, its variance reduced versions have…

Machine Learning · Computer Science 2022-11-22 Yuri Kinoshita , Taiji Suzuki

We consider the problem of analyzing and designing gradient-based discrete-time optimization algorithms for a class of unconstrained optimization problems having strongly convex objective functions with Lipschitz continuous gradient. By…

Optimization and Control · Mathematics 2025-10-20 Simon Michalowsky , Carsten Scherer , Christian Ebenbauer

Preconditioning is a crucial operation in gradient-based numerical optimisation. It helps decrease the local condition number of a function by appropriately transforming its gradient. For a convex function, where the gradient can be…

Optimization and Control · Mathematics 2023-08-29 Dmitrii A. Pasechnyuk , Alexander Gasnikov , Martin Takáč

Many large-scale constrained optimization problems can be formulated as bilevel distributed optimization tasks over undirected networks, where agents collaborate to minimize a global cost function while adhering to constraints, relying only…

Optimization and Control · Mathematics 2025-11-25 Ajay Tak , Mayank Baranwal

In this paper, we introduce various mechanisms to obtain accelerated first-order stochastic optimization algorithms when the objective function is convex or strongly convex. Specifically, we extend the Catalyst approach originally designed…

Optimization and Control · Mathematics 2019-10-10 Andrei Kulunchakov , Julien Mairal

In this paper we present an inexact zeroth-order method suitable for the solution nonsmooth and nonconvex stochastic composite optimization problems, in which the objective is split into a real-valued Lipschitz continuous stochastic…

Optimization and Control · Mathematics 2025-12-11 Spyridon Pougkakiotis , Dionysis Kalogerias

We focus on nonconvex and nonsmooth minimization problems with a composite objective, where the differentiable part of the objective is freed from the usual and restrictive global Lipschitz gradient continuity assumption. This longstanding…

Optimization and Control · Mathematics 2017-06-21 Jérôme Bolte , Shoham Sabach , Marc Teboulle , Yakov Vaisbourd

There is a recent surge of interest in nonconvex reformulations via low-rank factorization for stochastic convex semidefinite optimization problem in the purpose of efficiency and scalability. Compared with the original convex formulations,…

Optimization and Control · Mathematics 2018-02-27 Jinshan Zeng , Ke Ma , Yuan Yao

This paper proposes novel gradient-flow schemes that yield convergence to the optimal point of a convex optimization problem within a \textit{fixed} time from any given initial condition for unconstrained optimization, constrained…

Optimization and Control · Mathematics 2022-04-27 Kunal Garg , Dimitra Panagou