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SGD (Stochastic Gradient Descent) is a popular algorithm for large scale optimization problems due to its low iterative cost. However, SGD can not achieve linear convergence rate as FGD (Full Gradient Descent) because of the inherent…

Machine Learning · Computer Science 2017-12-05 Aixiang Chen , Bingchuan Chen , Xiaolong Chai , Rui Bian , Hengguang Li

We study a class of optimization problems in which the objective function is given by the sum of a differentiable but possibly nonconvex component and a nondifferentiable convex regularization term. We introduce an auxiliary variable to…

Optimization and Control · Mathematics 2019-08-27 Neil K. Dhingra , Sei Zhen Khong , Mihailo R. Jovanović

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

Stochastic Gradient (SG) is the defacto iterative technique to solve stochastic optimization (SO) problems with a smooth (non-convex) objective $f$ and a stochastic first-order oracle. SG's attractiveness is due in part to its simplicity of…

Optimization and Control · Mathematics 2024-03-08 David Newton , Raghu Bollapragada , Raghu Pasupathy , Nung Kwan Yip

A very popular approach for solving stochastic optimization problems is the stochastic gradient descent method (SGD). Although the SGD iteration is computationally cheap and the practical performance of this method may be satisfactory under…

Optimization and Control · Mathematics 2017-06-21 Andrei Patrascu , Ion Necoara

In this paper, we consider a general stochastic optimization problem which is often at the core of supervised learning, such as deep learning and linear classification. We consider a standard stochastic gradient descent (SGD) method with a…

Machine Learning · Statistics 2018-12-27 Lam M. Nguyen , Nam H. Nguyen , Dzung T. Phan , Jayant R. Kalagnanam , Katya Scheinberg

This paper explores numerical methods for solving a convex differentiable semi-infinite program. We introduce a primal-dual gradient method which performs three updates iteratively: a momentum gradient ascend step to update the constraint…

Optimization and Control · Mathematics 2024-07-23 Yao Yao , Qihang Lin , Tianbao Yang

We develop stochastic first-order primal-dual algorithms to solve a class of convex-concave saddle-point problems. When the saddle function is strongly convex in the primal variable, we develop the first stochastic restart scheme for this…

Optimization and Control · Mathematics 2021-04-13 Renbo Zhao

We consider a general multi-agent convex optimization problem where the agents are to collectively minimize a global objective function subject to a global inequality constraint, a global equality constraint, and a global constraint set.…

Optimization and Control · Mathematics 2011-05-13 Minghui Zhu , Sonia Martinez

In this work we investigate the practicality of stochastic gradient descent and recently introduced variants with variance-reduction techniques in imaging inverse problems. Such algorithms have been shown in the machine learning literature…

Optimization and Control · Mathematics 2021-01-26 Junqi Tang , Karen Egiazarian , Mohammad Golbabaee , Mike Davies

In this paper, we propose a proximal stochasitc gradient algorithm (PSGA) for solving composite optimization problems by incorporating variance reduction techniques and an adaptive step-size strategy. In the PSGA method, the objective…

Optimization and Control · Mathematics 2026-04-06 Changjie Fang , Hao Yang , Shenglan Chen

The mirror descent algorithm is known to be effective in situations where it is beneficial to adapt the mirror map to the underlying geometry of the optimization model. However, the effect of mirror maps on the geometry of distributed…

Optimization and Control · Mathematics 2024-03-13 Anastasia Borovykh , Nikolas Kantas , Panos Parpas , Grigorios A. Pavliotis

Stochastic gradient descent (SGD) is a widely used algorithm in machine learning, particularly for neural network training. Recent studies on SGD for canonical quadratic optimization or linear regression show it attains well generalization…

Machine Learning · Computer Science 2024-09-17 Haihan Zhang , Yuanshi Liu , Qianwen Chen , Cong Fang

A stochastic gradient method for finite-sum minimization subject to deterministic linear constraints is proposed and analyzed. The procedure presented adapts the projected gradient method on convex set to the use of both a stochastic…

Optimization and Control · Mathematics 2026-05-19 Natasa Krklec Jerinkic , Benedetta Morini , Mahsa Yousefi

Stochastic gradient methods (SGMs) have been extensively used for solving stochastic problems or large-scale machine learning problems. Recent works employ various techniques to improve the convergence rate of SGMs for both convex and…

Optimization and Control · Mathematics 2022-05-02 Yangyang Xu , Yibo Xu

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

In this work, we revisit a classical incremental implementation of the primal-descent dual-ascent gradient method used for the solution of equality constrained optimization problems. We provide a short proof that establishes the linear…

Optimization and Control · Mathematics 2020-01-17 Sulaiman A. Alghunaim , Ali H. Sayed

The stochastic gradient (SG) method can minimize an objective function composed of a large number of differentiable functions, or solve a stochastic optimization problem, to a moderate accuracy. The block coordinate descent/update (BCD)…

Optimization and Control · Mathematics 2015-11-23 Yangyang Xu , Wotao Yin

We study the computational complexity certification of inexact gradient augmented Lagrangian methods for solving convex optimization problems with complicated constraints. We solve the augmented Lagrangian dual problem that arises from the…

Optimization and Control · Mathematics 2013-02-19 Valentin Nedelcu , Ion Necoara , Quoc Tran Dinh

We consider stochastic convex optimization problems where the objective is an expectation over smooth functions. For this setting we suggest a novel gradient estimate that combines two recent mechanism that are related to notion of…

Machine Learning · Computer Science 2025-03-06 Tehila Dahan , Kfir Y. Levy