相关论文: Popov Mirror-Prox for solving Variational Inequali…

We study the problem of learning minimax policies in zero-sum matrix games. Fiegel et al. (2025) recently showed that achieving last-iterate convergence in this setting is harder when the players are uncoupled, by proving a lower bound on…

In this paper, the optimal convergence rate $O\left(N^{-1/2}\right)$ (where $N$ is the total number of iterations performed by the algorithm), without the presence of a logarithmic factor, is proved for mirror descent algorithms with…

The paper concerns optimization problems with general equality and inequality constraints and with constraints expressed by a convex set. In order to solve these problems, the general constraints are treated by an exact penalty functions…

The proximal extrapolated gradient method \cite{Malitsky18a} is an extension of the projected reflected gradient method \cite{Malitsky15}. Both methods were proposed for solving the classic variational inequalities. In this paper, we…

We study stochastic convex optimization under infinite noise variance. Specifically, when the stochastic gradient is unbiased and has uniformly bounded $(1+\kappa)$-th moment, for some $\kappa \in (0,1]$, we quantify the convergence rate of…

We consider the optimization problem of minimizing an objective functional, which admits a variational form and is defined over probability distributions on the constrained domain, which poses challenges to both theoretical analysis and…

We consider finding a zero point of the maximally monotone operator $T$. First, instead of using the proximal point algorithm (PPA) for this purpose, we employ PPA to solve its Yosida regularization $T_{\lambda}$. Then, based on an…

We develop a novel primal-dual algorithm to solve a class of nonsmooth and nonlinear compositional convex minimization problems, which covers many existing and brand-new models as special cases. Our approach relies on a combination of a new…

We propose a variable metric extension of the forward--backward-forward algorithm for finding a zero of the sum of a maximally monotone operator and a Lipschitzian monotone operator in Hilbert spaces. In turn, this framework provides a…

Path cover is a well-known intractable problem that finds a minimum number of vertex disjoint paths in a given graph to cover all the vertices. We show that a variant, where the objective function is not the number of paths but the number…

We fix a fundamental issue in the stochastic extragradient method by providing a new sampling strategy that is motivated by approximating implicit updates. Since the existing stochastic extragradient algorithm, called Mirror-Prox, of…

In this paper, we study variational inequality problems (VIPs) with involved mappings and feasible sets characterized by polynomial functions (namely, polynomial VIPs). We propose a numerical algorithm for computing solutions to polynomial…

In this paper, we first propose a general inertial proximal point method for the mixed variational inequality (VI) problem. Based on our knowledge, without stronger assumptions, convergence rate result is not known in the literature for…

Primal-dual algorithms are frequently used for iteratively solving large-scale convex optimization problems. The analysis of such algorithms is usually done on a case-by-case basis, and the resulting guaranteed rates of convergence can be…

The goal of this paper is to present two algorithms for solving systems of inclusion problems, with all component of the systems being a sum of two maximal monotone operators. The algorithms are variants of the forward-backward splitting…

In this paper, we study games with continuous action spaces and non-linear payoff functions. Our key insight is that Lipschitz continuity of the payoff function allows us to provide algorithms for finding approximate equilibria in these…

This paper combines two ingredients in order to get a rather surprising result on one of the most studied, elegant and powerful tools for solving convex feasibility problems, the method of alternating projections (MAP). Going back to names…

The vertex cover problem is a famous combinatorial problem, and its complexity has been heavily studied. While a 2-approximation can be trivially obtained for it, researchers have not been able to approximate it better than 2-\textit{o}(1).…

We study the problem of maximizing a continuous DR-submodular function that is not necessarily smooth. We prove that the continuous greedy algorithm achieves an $[(1-1/e)\OPT-\epsilon]$ guarantee when the function is monotone and…

Mirror descent plays a crucial role in constrained optimization and acceleration schemes, along with its corresponding low-resolution ordinary differential equations (ODEs) framework have been proposed. However, the low-resolution ODEs are…