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Related papers: Variance-Reduced Splitting Schemes for Monotone St…

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We propose a variation of the forward--backward splitting method for solving structured monotone inclusions. Our method integrates past iterates and two deviation vectors into the update equations. These deviation vectors bring flexibility…

Optimization and Control · Mathematics 2023-07-14 Hamed Sadeghi , Sebastian Banert , Pontus Giselsson

Monotone inclusions have a wide range of applications, including minimization, saddle-point, and equilibria problems. We introduce new stochastic algorithms, with or without variance reduction, to estimate a root of the expectation of…

Optimization and Control · Mathematics 2024-05-24 Abdurakhmon Sadiev , Laurent Condat , Peter Richtárik

We investigate the asymptotic behavior of a stochastic version of the forward-backward splitting algorithm for finding a zero of the sum of a maximally monotone set-valued operator and a cocoercive operator in Hilbert spaces. Our general…

Optimization and Control · Mathematics 2015-07-28 Patrick L. Combettes , Jean-Christophe Pesquet

In this paper, we study a class of stochastic and finite-sum convex optimization problems with deterministic constraints. Existing methods typically aim to find an $\epsilon$-$expectedly\ feasible\ stochastic\ optimal$ solution, in which…

Optimization and Control · Mathematics 2025-06-26 Zhaosong Lu , Yifeng Xiao

We present two modified versions of the primal-dual splitting algorithm relying on forward-backward splitting proposed in \cite{vu} for solving monotone inclusion problems. Under strong monotonicity assumptions for some of the operators…

Optimization and Control · Mathematics 2013-03-13 Radu Ioan Bot , Ernö Robert Csetnek , Andre Heinrich

We propose a multilevel stochastic approximation (MLSA) scheme for the computation of the value-at-risk (VaR) and expected shortfall (ES) of a financial loss, which can only be computed via simulations conditionally on the realisation of…

Computational Finance · Quantitative Finance 2026-04-14 Stéphane Crépey , Noufel Frikha , Azar Louzi

In this paper, we study smooth stochastic multi-level composition optimization problems, where the objective function is a nested composition of $T$ functions. We assume access to noisy evaluations of the functions and their gradients,…

Optimization and Control · Mathematics 2022-02-15 Krishnakumar Balasubramanian , Saeed Ghadimi , Anthony Nguyen

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

Minimizing finite sums of functions is a central problem in optimization, arising in numerous practical applications. Such problems are commonly addressed using first-order optimization methods. However, these procedures cannot be used in…

Optimization and Control · Mathematics 2025-07-01 Marco Rando , Cheik Traoré , Cesare Molinari , Lorenzo Rosasco , Silvia Villa

We aim to solve a structured convex optimization problem, where a nonsmooth function is composed with a linear operator. When opting for full splitting schemes, usually, primal-dual type methods are employed as they are effective and also…

Optimization and Control · Mathematics 2019-05-17 Radu Ioan Bot , Axel Böhm

This work presents an algorithmic scheme for solving the infinite-time constrained linear quadratic regulation problem. We employ an accelerated version of a popular proximal gradient scheme, commonly known as the Forward-Backward Splitting…

Optimization and Control · Mathematics 2015-01-20 Giorgos Stathopoulos , Milan Korda , Colin N. Jones

In this paper, we address variational inequalities (VI) with a finite-sum structure. We introduce a novel single-loop stochastic variance-reduced algorithm, incorporating the Bregman distance function, and establish an optimal convergence…

Optimization and Control · Mathematics 2025-07-22 Zeinab Alizadeh , Erfan Yazdandoost Hamedani , Afrooz Jalilzadeh

Multi-block separable convex problems recently received considerable attention. This class of optimization problems minimizes a separable convex objective function with linear constraints. The algorithmic challenges come from the fact that…

Optimization and Control · Mathematics 2016-08-18 Qia Li , Yuesheng Xu , Na Zhang

We introduce a generalized forward-backward splitting method with penalty term for solving monotone inclusion problems involving the sum of a finite number of maximally monotone operators and the normal cone to the nonempty set of zeros of…

Optimization and Control · Mathematics 2018-07-31 Nimit Nimana , Narin Petrot

This paper introduces a family of stochastic extragradient-type algorithms for a class of nonconvex-nonconcave problems characterized by the weak Minty variational inequality (MVI). Unlike existing results on extragradient methods in the…

Optimization and Control · Mathematics 2023-02-20 Thomas Pethick , Olivier Fercoq , Puya Latafat , Panagiotis Patrinos , Volkan Cevher

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

We propose and study a weakly convergent variant of the forward--backward algorithm for solving structured monotone inclusion problems. Our algorithm features a per-iteration deviation vector which provides additional degrees of freedom.…

Optimization and Control · Mathematics 2022-08-15 Hamed Sadeghi , Sebastian Banert , Pontus Giselsson

We analyze algorithms for solving stochastic variational inequalities (VI) without the bounded variance or bounded domain assumptions, where our main focus is min-max optimization with possibly unbounded constraint sets. We focus on two…

Optimization and Control · Mathematics 2026-02-06 Ahmet Alacaoglu , Jun-Hyun Kim

This paper delves into stochastic optimization problems that involve Markovian noise. We present a unified approach for the theoretical analysis of first-order gradient methods for stochastic optimization and variational inequalities. Our…

Optimization and Control · Mathematics 2024-04-02 Aleksandr Beznosikov , Sergey Samsonov , Marina Sheshukova , Alexander Gasnikov , Alexey Naumov , Eric Moulines

We investigate the convergence properties of a stochastic primal-dual splitting algorithm for solving structured monotone inclusions involving the sum of a cocoercive operator and a composite monotone operator. The proposed method is the…

Optimization and Control · Mathematics 2016-02-26 Lorenzo Rosasco , Silvia Villa , Bang Cong Vu