Related papers: A Hybrid Algorithm for Monotone Variational Inequa…
This work proposes a novel distributed approach for computing a Nash equilibrium in convex games with merely monotone and restricted strongly monotone pseudo-gradients. By leveraging the idea of the centralized operator extrapolation method…
It is known that adaptive optimization algorithms represent the key pillar behind the rise of the Machine Learning field. In the Optimization literature numerous studies have been devoted to accelerated gradient methods but only recently…
We study novel robust zero-order algorithms with acceleration for the solution of real-time optimization problems. In particular, we propose a family of extremum seeking dynamics that can be universally modeled as singularly perturbed…
Classically, a mainstream approach for solving a convex-concave min-max problem is to instead solve the variational inequality problem arising from its first-order optimality conditions. Is it possible to solve min-max problems faster by…
This paper is an attempt to remedy the problem of slow convergence for first-order numerical algorithms by proposing an adaptive conditioning heuristic. First, we propose a parallelizable numerical algorithm that is capable of solving…
The paper starts with a concise description of the recently developed semismooth* Newton method for the solution of general inclusions. This method is then applied to a class of variational inequalities of the second kind. As a result, one…
An efficient proximal-gradient-based method, called proximal extrapolated gradient method, is designed for solving monotone variational inequality in Hilbert space. The proposed method extends the acceptable range of parameters to obtain…
Basing on some recently proposed methods for solving variational inequalities with non-smooth operators, we propose an analogue of the Mirror Prox method for the corresponding class of problems under the assumption of relative smoothness…
In this paper, we propose a unifying framework incorporating several momentum-related search directions for solving strongly monotone variational inequalities. The specific combinations of the search directions in the framework are made to…
This paper investigates the equilibrium convergence properties of a proposed algorithm for potential games with continuous strategy spaces in the presence of feedback delays, a main challenge in multi-agent systems that compromises the…
Although adaptive optimization algorithms have been successful in many applications, there are still some mysteries in terms of convergence analysis that have not been unraveled. This paper provides a novel non-convex analysis of adaptive…
In recent years, even though Stochastic Gradient Descent (SGD) and its variants are well-known for training neural networks, it suffers from limitations such as the lack of theoretical guarantees, vanishing gradients, and excessive…
We propose a variant of the classical conditional gradient method for sparse inverse problems with differentiable measurement models. Such models arise in many practical problems including superresolution, time-series modeling, and matrix…
We study a bilevel variational inequality problem where the feasible set is itself the solution set of another variational inequality. Motivated by the difficulty of computing projections onto such sets, we consider a regularized…
An adaptive analogue of the Yu. E. Nesterov method for variational inequalities with a strongly monotone operator is proposed. Some estimates are obtained for the parameters determining the quality of the solution of the variational…
We propose a novel randomized incremental gradient algorithm, namely, VAriance-Reduced Accelerated Gradient (Varag), for finite-sum optimization. Equipped with a unified step-size policy that adjusts itself to the value of the condition…
We propose a novel continuous-time algorithm for inequality-constrained convex optimization inspired by proportional-integral control. Unlike the popular primal-dual gradient dynamics, our method includes a proportional term to control the…
The aim of this paper is to present an extragradient method for variational inequality associated to a point-to-set vector field in Hadamard manifolds and to study its convergence properties. In order to present our method the concept of…
The objective of this research is to explore a convex feasibility problem, which consists of a monotone variational inequality problem and a fixed point problem. We introduce four inertial extragradient algorithms that are motivated by the…
Learning from repeated play in a fixed two-player zero-sum game is a classic problem in game theory and online learning. We consider a variant of this problem where the game payoff matrix changes over time, possibly in an adversarial…