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Lower-bound analyses for nonconvex strongly-concave minimax optimization problems have shown that stochastic first-order algorithms require at least $\mathcal{O}(\varepsilon^{-4})$ oracle complexity to find an $\varepsilon$-stationary…

Machine Learning · Computer Science 2025-05-15 Haoyuan Cai , Sulaiman A. Alghunaim , Ali H. Sayed

In a real Hilbert space setting, we study the convergence properties of an inexact gradient algorithm featuring both viscous and Hessian driven damping for convex differentiable optimization. In this algorithm, the gradient evaluation can…

Optimization and Control · Mathematics 2025-09-25 Harsh Choudhary , Jalal Fadili , Vyachelav Kungurtsev

In this paper, we study the convergence properties of the Stochastic Gradient Descent (SGD) method for finding a stationary point of a given objective function $J(\cdot)$. The objective function is not required to be convex. Rather, our…

Machine Learning · Statistics 2024-09-24 Rajeeva L. Karandikar , M. Vidyasagar

Composite optimization offers a powerful modeling tool for a variety of applications and is often numerically solved by means of proximal gradient methods. In this paper, we consider fully nonconvex composite problems under only local…

Optimization and Control · Mathematics 2023-02-09 Alberto De Marchi , Andreas Themelis

We consider the problem of global optimization of an unknown non-convex smooth function with zeroth-order feedback. In this setup, an algorithm is allowed to adaptively query the underlying function at different locations and receives noisy…

Machine Learning · Statistics 2018-03-26 Yining Wang , Sivaraman Balakrishnan , Aarti Singh

We analyze the complexity of biased stochastic gradient methods (SGD), where individual updates are corrupted by deterministic, i.e. biased error terms. We derive convergence results for smooth (non-convex) functions and give improved rates…

Machine Learning · Computer Science 2021-05-11 Ahmad Ajalloeian , Sebastian U. Stich

In this paper, we study a family of non-convex and possibly non-smooth inf-projection minimization problems, where the target objective function is equal to minimization of a joint function over another variable. This problem include…

Machine Learning · Computer Science 2020-07-15 Yan Yan , Yi Xu , Lijun Zhang , Xiaoyu Wang , Tianbao Yang

We consider stochastic convex optimization with a strongly convex (but not necessarily smooth) objective. We give an algorithm which performs only gradient updates with optimal rate of convergence.

Optimization and Control · Mathematics 2010-06-15 Elad Hazan , Satyen Kale

We study the complexity of producing $(\delta,\epsilon)$-stationary points of Lipschitz objectives which are possibly neither smooth nor convex, using only noisy function evaluations. Recent works proposed several stochastic zero-order…

Optimization and Control · Mathematics 2024-04-16 Guy Kornowski , Ohad Shamir

We consider the problem of minimizing a continuous function given quantum access to a stochastic gradient oracle. We provide two new methods for the special case of minimizing a Lipschitz convex function. Each method obtains a dimension…

Quantum Physics · Physics 2024-07-26 Aaron Sidford , Chenyi Zhang

The stochastic gradient descent has been widely used for solving composite optimization problems in big data analyses. Many algorithms and convergence properties have been developed. The composite functions were convex primarily and…

Machine Learning · Statistics 2020-03-03 Takayuki Kawashima , Hironori Fujisawa

An usual problem in statistics consists in estimating the minimizer of a convex function. When we have to deal with large samples taking values in high dimensional spaces, stochastic gradient algorithms and their averaged versions are…

Statistics Theory · Mathematics 2022-01-12 Antoine Godichon-Baggioni

Gradient compression is of growing interests for solving constrained optimization problems including compressed sensing, noisy recovery and matrix completion under limited communication resources and storage costs. Convergence analysis of…

Optimization and Control · Mathematics 2024-10-30 Zhaoyue Xia , Jun Du , Chunxiao Jiang , H. Vincent Poor , Yong Ren

In this paper, we consider a class of constrained multiobjective optimization problems, where each objective function can be expressed by adding a possibly nonsmooth nonconvex function and a differentiable function with Lipschitz continuous…

Optimization and Control · Mathematics 2026-01-01 Nguyen Van Tuyen , Minh N. Dao , Tran Van Nghi

The paper is devoted to new modifications of recently proposed adaptive methods of Mirror Descent for convex minimization problems in the case of several convex functional constraints. Methods for problems of two classes are considered. The…

Optimization and Control · Mathematics 2018-05-29 Fedor S. Stonyakin , Mohammad S. Alkousa , Alexey N. Stepanov , Maxim A. Barinov

This paper investigates a category of constrained fractional optimization problems that emerge in various practical applications. The objective function for this category is characterized by the ratio of a numerator and denominator, both…

Optimization and Control · Mathematics 2026-05-28 Yizun Lin , Jian-Feng Cai , Zhao-Rong Lai , Cheng Li

This work aims to solve a stochastic nonconvex nonsmooth composite optimization problem. Previous works on composite optimization problem requires the major part to satisfy Lipschitz smoothness or some relaxed smoothness conditions, which…

Optimization and Control · Mathematics 2025-10-07 Ziyi Chen , Peiran Yu , Heng Huang

The minimization of convex objectives coming from linear supervised learning problems, such as penalized generalized linear models, can be formulated as finite sums of convex functions. For such problems, a large set of stochastic…

Machine Learning · Statistics 2018-12-18 Martin Bompaire , Emmanuel Bacry , Stéphane Gaïffas

This work explores a novel perspective on solving nonconvex and nonsmooth optimization problems by leveraging sampling based methods. Instead of treating the objective function purely through traditional (often deterministic) optimization…

Optimization and Control · Mathematics 2025-05-21 Nahom Seyoum , Haoxiang You

We consider non-smooth saddle point optimization problems. To solve these problems, we propose a zeroth-order method under bounded or Lipschitz continuous noise, possible adversarial. In contrast to the state-of-the-art algorithms, our…

Optimization and Control · Mathematics 2023-03-28 Darina Dvinskikh , Vladislav Tominin , Yaroslav Tominin , Alexander Gasnikov