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We present and study the iteration-complexity of a relative-error inexact proximal-Newton extragradient algorithm for solving smooth monotone variational inequality problems in real Hilbert spaces. We removed a search procedure from…

Optimization and Control · Mathematics 2024-04-16 M. Marques Alves , João M. Pereira , Benar F. Svaiter

The subgradient method is one of the most fundamental algorithmic schemes for nonsmooth optimization. The existing complexity and convergence results for this method are mainly derived for Lipschitz continuous objective functions. In this…

Optimization and Control · Mathematics 2024-11-01 Xiao Li , Lei Zhao , Daoli Zhu , Anthony Man-Cho So

We analyze stochastic gradient algorithms for optimizing nonconvex, nonsmooth finite-sum problems. In particular, the objective function is given by the summation of a differentiable (possibly nonconvex) component, together with a possibly…

Optimization and Control · Mathematics 2018-12-04 Zhize Li , Jian Li

We consider minimization of a smooth nonconvex function with inexact oracle access to gradient and Hessian (without assuming access to the function value) to achieve approximate second-order optimality. A novel feature of our method is that…

Optimization and Control · Mathematics 2024-03-27 Shuyao Li , Stephen J. Wright

We propose stochastic variance reduced algorithms for solving convex-concave saddle point problems, monotone variational inequalities, and monotone inclusions. Our framework applies to extragradient, forward-backward-forward, and…

Optimization and Control · Mathematics 2022-06-14 Ahmet Alacaoglu , Yura Malitsky

Derivative-free optimization has become an important technique used in machine learning for optimizing black-box models. To conduct updates without explicitly computing gradient, most current approaches iteratively sample a random search…

Machine Learning · Statistics 2018-08-03 Liu Liu , Minhao Cheng , Cho-Jui Hsieh , Dacheng Tao

We consider the unconstrained optimization problem whose objective function is composed of a smooth and a non-smooth conponents where the smooth component is the expectation a random function. This type of problem arises in some interesting…

Optimization and Control · Mathematics 2011-07-01 Qihang Lin , Xi Chen , Javier Pena

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

We present a variant of accelerated gradient descent algorithms, adapted from Nesterov's optimal first-order methods, for weakly-quasi-convex and weakly-quasi-strongly-convex functions. We show that by tweaking the so-called estimate…

Optimization and Control · Mathematics 2020-06-16 Jingjing Bu , Mehran Mesbahi

This paper considers stochastic subgradient mirror-descent method for solving constrained convex minimization problems. In particular, a stochastic subgradient mirror-descent method with weighted iterate-averaging is investigated and its…

Optimization and Control · Mathematics 2013-07-09 Angelia Nedich , Soomin Lee

This paper considers stochastic convex optimization problems with smooth functional constraints arising in constrained estimation and robust signal recovery. We operate in the high-dimensional and highly-constrained setting, where oracle…

Optimization and Control · Mathematics 2025-12-16 Vaibhav Rajoriya , Prateek Priyaranjan Pradhan , Ketan Rajawat

We investigate a structured class of nonconvex-nonconcave min-max problems exhibiting so-called \emph{weak Minty} solutions, a notion which was only recently introduced, but is able to simultaneously capture different generalizations of…

Optimization and Control · Mathematics 2023-06-21 Axel Böhm

In this work, we examine sampling problems with non-smooth potentials. We propose a novel Markov chain Monte Carlo algorithm for sampling from non-smooth potentials. We provide a non-asymptotical analysis of our algorithm and establish a…

Machine Learning · Computer Science 2022-02-11 Jiaming Liang , Yongxin Chen

In this paper, we address stochastic optimization problems involving a composition of a non-smooth outer function and a smooth inner function, a formulation frequently encountered in machine learning and operations research. To deal with…

Optimization and Control · Mathematics 2026-05-15 Tommaso Giovannelli , Jingfu Tan , Luis Nunes Vicente

The constrained gradient method (CGM) has recently been proposed to solve convex optimization and monotone variational inequality (VI) problems with general functional constraints. While existing literature has established convergence…

Optimization and Control · Mathematics 2025-11-24 Danqing Zhou , Hongmei Chen , Shiqian Ma , Junfeng Yang

We study structured convex optimization problems, with additive objective $r:=p + q$, where $r$ is ($\mu$-strongly) convex, $q$ is $L_q$-smooth and convex, and $p$ is $L_p$-smooth, possibly nonconvex. For such a class of problems, we…

Optimization and Control · Mathematics 2022-05-31 Dmitry Kovalev , Aleksandr Beznosikov , Ekaterina Borodich , Alexander Gasnikov , Gesualdo Scutari

In this paper, we propose a general extra-gradient scheme for solving monotone variational inequalities (VI), referred to here as Approximation-based Regularized Extra-gradient method (ARE). The first step of ARE solves a VI subproblem with…

Optimization and Control · Mathematics 2022-10-11 Kevin Huang , Shuzhong Zhang

The paper investigates two inertial extragradient algorithms for seeking a common solution to a variational inequality problem involving a monotone and Lipschitz continuous mapping and a fixed point problem with a demicontractive mapping in…

Optimization and Control · Mathematics 2023-08-08 Bing Tan , Liya Liu , Xiaolong Qin

We consider stochastic variational inequalities with monotone operators defined as the expected value of a random operator. We assume the feasible set is the intersection of a large family of convex sets. We propose a method that combines…

Optimization and Control · Mathematics 2017-03-03 Alfredo Iusem , Alejandro Jofré , Philip Thompson

We consider the problem of optimizing the sum of a smooth convex function and a non-smooth convex function using proximal-gradient methods, where an error is present in the calculation of the gradient of the smooth term or in the proximity…

Machine Learning · Computer Science 2011-12-02 Mark Schmidt , Nicolas Le Roux , Francis Bach