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We propose a novel adaptive, accelerated algorithm for the stochastic constrained convex optimization setting. Our method, which is inspired by the Mirror-Prox method, \emph{simultaneously} achieves the optimal rates for smooth/non-smooth…

Optimization and Control · Mathematics 2019-10-31 Ali Kavis , Kfir Y. Levy , Francis Bach , Volkan Cevher

This paper is devoted to the theoretical and numerical investigation of an augmented Lagrangian method for the solution of optimization problems with geometric constraints. Specifically, we study situations where parts of the constraints…

Optimization and Control · Mathematics 2022-04-20 Xiaoxi Jia , Christian Kanzow , Patrick Mehlitz , Gerd Wachsmuth

This paper proposes a novel first-order algorithm that solves composite nonsmooth and stochastic convex optimization problem with function constraints. Most of the works in the literature provide convergence rate guarantees on the…

Optimization and Control · Mathematics 2024-10-25 Digvijay Boob , Mohammad Khalafi

In this paper, we propose two algorithms for solving convex optimization problems with linear ascending constraints. When the objective function is separable, we propose a dual method which terminates in a finite number of iterations. In…

Optimization and Control · Mathematics 2014-09-26 Zizhuo Wang

In this paper, we propose a unified view of gradient-based algorithms for stochastic convex composite optimization by extending the concept of estimate sequence introduced by Nesterov. This point of view covers the stochastic gradient…

Machine Learning · Statistics 2019-05-08 Andrei Kulunchakov , Julien Mairal

We develop universal gradient methods for Stochastic Convex Optimization (SCO). Our algorithms automatically adapt not only to the oracle's noise but also to the H\"older smoothness of the objective function without a priori knowledge of…

Optimization and Control · Mathematics 2024-07-12 Anton Rodomanov , Ali Kavis , Yongtao Wu , Kimon Antonakopoulos , Volkan Cevher

Provably solving stochastic convex optimization problems with constraints is essential for various problems in science, business, and statistics. Recently proposed XOR-Stochastic Gradient Descent (XOR-SGD) provides a convergence rate…

Optimization and Control · Mathematics 2022-03-23 Fan Ding , Yijie Wang , Jianzhu Ma , Yexiang Xue

Gradient descent methods are fundamental first-order optimization algorithms in both Euclidean spaces and Riemannian manifolds. However, the exact gradient is not readily available in many scenarios. This paper proposes a novel inexact…

Optimization and Control · Mathematics 2024-09-18 Juan Zhou , Kangkang Deng , Hongxia Wang , Zheng Peng

This paper presents new first-order methods for achieving optimal oracle complexities in convex optimization with convex functional constraints. Oracle complexities are measured by the number of function and gradient evaluations. To achieve…

Optimization and Control · Mathematics 2026-04-17 Qi Deng , Guanghui Lan , Zhenwei Lin

In this paper, we present a conditional gradient type (CGT) method for solving a class of composite optimization problems where the objective function consists of a (weakly) smooth term and a (strongly) convex regularization term. While…

Optimization and Control · Mathematics 2018-01-03 Saeed Ghadimi

We propose a novel stochastic smoothing accelerated gradient (SSAG) method for general constrained nonsmooth convex composite optimization, and analyze the convergence rates. The SSAG method allows various smoothing techniques, and can deal…

Optimization and Control · Mathematics 2026-02-03 Ruyu Wang , Chao Zhang

The graduated optimization approach, also known as the continuation method, is a popular heuristic to solving non-convex problems that has received renewed interest over the last decade. Despite its popularity, very little is known in terms…

Machine Learning · Computer Science 2015-07-28 Elad Hazan , Kfir Y. Levy , Shai Shalev-Shwartz

In this paper, we consider Nesterov's Accelerated Gradient method for solving Nonlinear Inverse and Ill-Posed Problems. Known to be a fast gradient-based iterative method for solving well-posed convex optimization problems, this method also…

Numerical Analysis · Mathematics 2020-01-13 Simon Hubmer , Ronny Ramlau

In this paper we consider stochastic composite convex optimization problems with the objective function satisfying a stochastic bounded gradient condition, with or without a quadratic functional growth property. These models include the…

Optimization and Control · Mathematics 2020-03-10 Ion Necoara

We introduce a detailed analysis of the convergence of first-order methods with composite noise (sum of relative and absolute) in gradient for convex and smooth function minimization. This paper illustrates instances of practical problems…

Optimization and Control · Mathematics 2026-03-16 Artem Vasin , Alexander Gasnikov

In this paper, we study a class of stochastic bilevel optimization problems, also known as stochastic simple bilevel optimization, where we minimize a smooth stochastic objective function over the optimal solution set of another stochastic…

Optimization and Control · Mathematics 2023-08-16 Jincheng Cao , Ruichen Jiang , Nazanin Abolfazli , Erfan Yazdandoost Hamedani , Aryan Mokhtari

Algorithmic reproducibility measures the deviation in outputs of machine learning algorithms upon minor changes in the training process. Previous work suggests that first-order methods would need to trade-off convergence rate (gradient…

Machine Learning · Computer Science 2024-01-11 Liang Zhang , Junchi Yang , Amin Karbasi , Niao He

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

Many statistical estimation procedures lead to nonconvex optimization problems. Algorithms to solve these are often guaranteed to output a stationary point of the optimization problem. Oracle inequalities are an important theoretical…

Statistics Theory · Mathematics 2018-02-28 Andreas Elsener , Sara van de Geer

This paper examines a variety of classical optimization problems, including well-known minimization tasks and more general variational inequalities. We consider a stochastic formulation of these problems, and unlike most previous work, we…

Optimization and Control · Mathematics 2025-11-11 Vladimir Solodkin , Andrew Veprikov , Aleksandr Beznosikov