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Two classes of methods have been proposed for escaping from saddle points with one using the second-order information carried by the Hessian and the other adding the noise into the first-order information. The existing analysis for…

Optimization and Control · Mathematics 2018-03-05 Yi Xu , Rong Jin , Tianbao Yang

In this paper, we present a unified analysis of methods for such a wide class of problems as variational inequalities, which includes minimization problems and saddle point problems. We develop our analysis on the modified Extra-Gradient…

Optimization and Control · Mathematics 2023-04-18 Aleksandr Beznosikov , Alexander Gasnikov , Karina Zainulina , Alexander Maslovskiy , Dmitry Pasechnyuk

In this paper, a novel stochastic extra-step quasi-Newton method is developed to solve a class of nonsmooth nonconvex composite optimization problems. We assume that the gradient of the smooth part of the objective function can only be…

Optimization and Control · Mathematics 2019-10-22 Minghan Yang , Andre Milzarek , Zaiwen Wen , Tong Zhang

We develop two novel stochastic variance-reduction methods to approximate solutions of a class of nonmonotone [generalized] equations. Our algorithms leverage a new combination of ideas from the forward-reflected-backward splitting method…

Optimization and Control · Mathematics 2025-05-30 Quoc Tran-Dinh

We study a class of second order variational inequalities with bilateral constraints. Under certain conditions we show the existence of a unique viscosity solution of these variational inequalities and give a stochastic representation to…

Analysis of PDEs · Mathematics 2007-05-23 Mrinal K Ghosh , K S Mallikarjuna Rao

This paper focuses on stochastic saddle point problems with decision-dependent distributions. These are problems whose objective is the expected value of a stochastic payoff function and whose data distribution drifts in response to…

Optimization and Control · Mathematics 2022-11-15 Killian Wood , Emiliano Dall'Anese

In this paper, we develop stochastic variance reduced algorithms for solving a class of finite-sum hemivariational inequality (HVI) problem. In this HVI problem, the associated function is assumed to be differentiable, and both the vector…

Optimization and Control · Mathematics 2025-09-12 Kevin Huang , Nuozhou Wang , Shuzhong Zhang

In this paper, we propose an Anderson-accelerated stochastic extragradient algorithm for solving a class of stochastic variational inequalities, by incorporating Anderson acceleration into the stochastic extragradient method under a…

Optimization and Control · Mathematics 2026-05-27 Xin Qu , Wei Bian , Xiaojun Chen

We consider monotone inclusion problems where the operators may be expectation-valued, a class of problems that subsumes convex stochastic optimization problems as well as subclasses of stochastic variational inequality and equilibrium…

Optimization and Control · Mathematics 2021-10-19 Shisheng Cui , Uday V. Shanbhag

Stochastic nonconvex minimax problems have attracted wide attention in machine learning, signal processing and many other fields in recent years. In this paper, we propose an accelerated first-order regularized momentum descent ascent…

Optimization and Control · Mathematics 2024-10-16 Huiling Zhang , Zi Xu

We consider a class of stochastic gradient optimization schemes. Assuming that the objective function is strongly convex, we prove weak error estimates which are uniform in time for the error between the solution of the numerical scheme,…

Numerical Analysis · Mathematics 2026-01-27 Charles-Edouard Bréhier , Marc Dambrine , Nassim En-Nebbazi

In this paper, we propose a stochastic method for solving equality constrained optimization problems that utilizes predictive variance reduction. Specifically, we develop a method based on the sequential quadratic programming paradigm that…

Optimization and Control · Mathematics 2023-03-28 Albert S. Berahas , Jiahao Shi , Zihong Yi , Baoyu Zhou

In this paper, we propose two novel non-stationary first-order primal-dual algorithms to solve nonsmooth composite convex optimization problems. Unlike existing primal-dual schemes where the parameters are often fixed, our methods use…

Optimization and Control · Mathematics 2020-07-13 Quoc Tran-Dinh , Yuzixuan Zhu

The article is devoted to the development of numerical methods for solving saddle point problems and variational inequalities with simplified requirements for the smoothness conditions of functionals. Recently there were proposed some…

Optimization and Control · Mathematics 2023-11-22 Alexander Titov , Fedor Stonyakin , Mohammad Alkousa , Alexander Gasnikov

In this paper, we propose practical normalized stochastic first-order methods with Polyak momentum, multi-extrapolated momentum, and recursive momentum for solving unconstrained optimization problems. These methods employ dynamically…

Optimization and Control · Mathematics 2026-02-12 Chuan He , Zhaosong Lu , Defeng Sun , Zhanwang Deng

Optimal prediction (OP) methods compensate for a lack of resolution in the numerical solution of complex problems through the use of an invariant measure as a prior measure in the Bayesian sense. In first-order OP, unresolved information is…

Numerical Analysis · Mathematics 2025-10-20 John Bell , Alexandre J. Chorin , William Crutchfield

This paper presents a novel approach to solving large-scale minimax problems with nonsmooth regularizers. We propose a stochastic implicit proximal point algorithm with variance reduction techniques where stochastic oracles are selected in…

Optimization and Control · Mathematics 2026-05-25 Kehan Zhu , Jiani Wang , Yu-Hong Dai

In this paper we analyze a zeroth-order proximal stochastic gradient method suitable for the minimization of weakly convex stochastic optimization problems. We consider nonsmooth and nonlinear stochastic composite problems, for which…

Optimization and Control · Mathematics 2025-04-21 Spyridon Pougkakiotis , Dionysios S. Kalogerias

In this paper, we present a novel stochastic method for solving variational inequalities (VI) in the context of Markovian noise. By leveraging Extragradient technique, we can productively solve VI optimization problems characterized by…

Optimization and Control · Mathematics 2026-05-18 Vladimir Solodkin , Michael Ermoshin , Roman Gavrilenko , Aleksandr Beznosikov

We study convex composite optimization problems, where the objective function is given by the sum of a prox-friendly function and a convex function whose subgradients are estimated under heavy-tailed noise. Existing work often employs…

Optimization and Control · Mathematics 2025-10-14 Chuan He , Zhaosong Lu