相关论文: Variance-reduction for Variational Inequality Prob…

Matrix Factorization is a popular non-convex optimization problem, for which alternating minimization schemes are mostly used. They usually suffer from the major drawback that the solution is biased towards one of the optimization…

This paper introduces adaptive Bregman proximal gradient algorithms for solving convex composite minimization problems without relying on global relative smoothness or strong convexity assumptions. Building upon recent advances in adaptive…

We propose a new class of fast Krasnoselkii--Mann methods with variance reduction to solve a finite-sum co-coercive equation $Gx = 0$. Our algorithm is single-loop and leverages a new family of unbiased variance-reduced estimators…

We improve the understanding of the $\textit{golden ratio algorithm}$, which solves monotone variational inequalities (VI) and convex-concave min-max problems via the distinctive feature of adapting the step sizes to the local Lipschitz…

We study a general convex optimization problem, which covers various classic problems in different areas and particularly includes many optimal transport related problems arising in recent years. To solve this problem, we revisit the…

We consider a stochastic Inverse Variational Inequality (IVI) problem defined by a continuous and co-coercive map over a closed and convex set. Motivated by the absence of performance guarantees for stochastic IVI, we present a…

In this paper we suggest a modification of the regression-based variance reduction approach recently proposed in Belomestny et al. This modification is based on the stratification technique and allows for a further significant variance…

This paper establishes the convergence properties of the Popov mirror-prox algorithm for solving stochastic and deterministic variational inequalities (VIs) under a polynomial growth condition on the mapping variation. Unlike existing…

The paper presents a fully explicit algorithm for monotone variational inequalities. The method uses variable stepsizes that are computed using two previous iterates as an approximation of the local Lipschitz constant without running a…

We study optimization of finite sums of geodesically smooth functions on Riemannian manifolds. Although variance reduction techniques for optimizing finite-sums have witnessed tremendous attention in the recent years, existing work is…

We consider variational inequalities coming from monotone operators, a setting that includes convex minimization and convex-concave saddle-point problems. We assume an access to potentially noisy unbiased values of the monotone operators…

Bilinear matrix inequality (BMI) problems in system and control designs are investigated in this paper. A solution method of reduction of variables (MRVs) is proposed. This method consists of a principle of variable classification, a…

A general deterministic analysis to state the necessary conditions with a coefficient determination for the variational source condition to hold is provided. Of particular interest in terms of the choice of the regularization parameter, it…

We introduce two algorithms for nonconvex regularized finite sum minimization, where typical Lipschitz differentiability assumptions are relaxed to the notion of relative smoothness. The first one is a Bregman extension of Finito/MISO,…

Yang et al. (2023) recently showed how to use first-order gradient methods to solve general variational inequalities (VIs) under a limiting assumption that analytic solutions of specific subproblems are available. In this paper, we…

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.…

We consider decentralized time-varying stochastic optimization problems where each of the functions held by the nodes has a finite sum structure. Such problems can be efficiently solved using variance reduction techniques. Our aim is to…

In this paper we consider convergence rate problems for stochastic strongly-convex optimization in the non-Euclidean sense with a constraint set over a time-varying multi-agent network. We propose two efficient non-Euclidean stochastic…

This paper considers variational inequalities (VI) defined by the conditional value-at-risk (CVaR) of uncertain functions and provides three stochastic approximation schemes to solve them. All methods use an empirical estimate of the CVaR…

Monotone operator splitting is a powerful paradigm that facilitates parallel processing for optimization problems where the cost function can be split into two convex functions. We propose a generalized form of monotone operator splitting…