English
Related papers

Related papers: Beyond Monotone Variational Inequalities: Solution…

200 papers

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…

Optimization and Control · Mathematics 2022-12-29 Ahmet Alacaoglu , Axel Böhm , Yura Malitsky

In this paper, we generalize the classical extragradient algorithm for solving variational inequality problems by utilizing nonzero normal vectors of the feasible set. In particular, conceptual algorithms are proposed with two different…

Optimization and Control · Mathematics 2019-02-25 J. Y. Bello Cruz , R. Díaz Millán , Hung M. Phan

While Variational Inequality (VI) is a well-established mathematical framework that subsumes Nash equilibrium and saddle-point problems, less is known about its extension, Quasi-Variational Inequalities (QVI). QVI allows for cases where the…

Optimization and Control · Mathematics 2025-11-25 Zeinab Alizadeh , Afrooz Jalilzadeh

In this paper, we propose two new solution schemes to solve the stochastic strongly monotone variational inequality problems: the stochastic extra-point solution scheme and the stochastic extra-momentum solution scheme. The first one is a…

Optimization and Control · Mathematics 2021-07-20 Kevin Huang , Shuzhong Zhang

We study monotone variational inequalities that can arise as optimality conditions for constrained convex optimisation or convex-concave minimax problems and propose a novel algorithm that uses only one gradient/operator evaluation and one…

Optimization and Control · Mathematics 2023-07-24 Michael Sedlmayer , Dang-Khoa Nguyen , Radu Ioan Bot

We propose novel high-order algorithms for a class of $\ell_p$-structured non-monotone variational inequalities. In particular, work by Diakonikolas et al. (2021), which introduced the weak Minty variational inequality (weak-MVI) setting,…

Optimization and Control · Mathematics 2026-03-17 Abhijeet Vyas , Brian Bullins

In this paper we consider a non-monotone (mixed) variational inequality model with (nonlinear) convex conic constraints. Through developing an equivalent Lagrangian function-like primal-dual saddle-point system for the VI model in question,…

Optimization and Control · Mathematics 2023-06-05 Lei Zhao , Daoli Zhu , Shuzhong Zhang

In this paper we propose new algorithms for solving a class of structured monotone variational inequality (VI) problems over compact feasible sets. By identifying the gradient components existing in the operator of VI, we show that it is…

Optimization and Control · Mathematics 2021-11-02 Guanghui Lan , Yuyuan Ouyang

Monotone variational inequalities (VIs) provide a unifying framework for convex minimization, equilibrium computation, and convex-concave saddle-point problems. Extragradient-type methods are among the most effective first-order algorithms…

Optimization and Control · Mathematics 2026-04-16 Lingqing Shen , Fatma Kılınç-Karzan

Variational inequalities (VIs) encompass many fundamental problems in diverse areas ranging from engineering to economics and machine learning. However, their considerable expressivity comes at the cost of computational intractability. In…

Computer Science and Game Theory · Computer Science 2025-03-03 Brian Hu Zhang , Ioannis Anagnostides , Emanuel Tewolde , Ratip Emin Berker , Gabriele Farina , Vincent Conitzer , Tuomas Sandholm

In this paper, we propose a general extra-gradient scheme for solving monotone variational inequalities (VI), referred to here as Approximation-based Regularized Extra-gradient method (ARE). The first step of ARE solves a VI subproblem with…

Optimization and Control · Mathematics 2022-10-11 Kevin Huang , Shuzhong Zhang

In this paper, we prove the existence of minimizers of a class of multi-constrained variational problems. We consider systems involving a nonlinearity that does not satisfy compactness, monotonicity, neither symmetry properties. Our…

Analysis of PDEs · Mathematics 2013-10-10 Hichem Hajaiej , Peter A. Markowich , Saber Trabelsi

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

The paper investigates two inertial extragradient algorithms for seeking a common solution to a variational inequality problem involving a monotone and Lipschitz continuous mapping and a fixed point problem with a demicontractive mapping in…

Optimization and Control · Mathematics 2023-08-08 Bing Tan , Liya Liu , Xiaolong Qin

We consider the mirror-prox algorithm for solving monotone Variational Inequality (VI) problems. As the mirror-prox algorithm is not practically implementable, except in special instances of VIs (such as affine VIs), we consider its…

Optimization and Control · Mathematics 2024-09-27 Abhishek Chakraborty , Angelia Nedić

In this paper, we study a class of misspecified variational inequalities (VIs) where both the monotone operator and nonlinear convex constraints depend on an unknown parameter learned via a secondary VI. Existing data-driven VI methods…

Optimization and Control · Mathematics 2026-03-18 Novel Kumar Dey , Mohammad Mahdi Ahmadi , Erfan Yazdandoost Hamedani , Afrooz Jalilzadeh

This paper is devoted to the variational inequality problems. We consider two classes of problems, the first is classical constrained variational inequality and the second is the same problem with functional (inequality type) constraints.…

Optimization and Control · Mathematics 2025-06-04 Mohammad S. Alkousa , Belal A. Alashqar , Fedor S. Stonyakin , Tarek Nabhani , Seydamet S. Ablaev

The constrained gradient method (CGM) has recently been proposed to solve convex optimization and monotone variational inequality (VI) problems with general functional constraints. While existing literature has established convergence…

Optimization and Control · Mathematics 2025-11-24 Danqing Zhou , Hongmei Chen , Shiqian Ma , Junfeng Yang

In this paper we study the bounded perturbation resilience of the extragradient and the subgradient extragradient methods for solving variational inequality (VI) problem in real Hilbert spaces. This is an important property of algorithms…

Optimization and Control · Mathematics 2017-11-20 Qiao-Li Dong , Aviv Gibali , Dan Jiang , Yu-Chao Tang

In this paper, we introduce and study a class of resolvent dynamical systems to investigate some inertial proximal methods for solving mixed variational inequalities. These proposed methods along with their discretizations and derived rates…

Dynamical Systems · Mathematics 2024-06-28 Oday Hazaimah