On Fixed-Time Stability of Continuous Dynamics for Non-Monotone Variational Inequalities
Abstract
Non-monotone variational inequalities (NMVI) are an important class of problems that generalize non-convex optimization and have various applications in optimization theory, machine learning, game theory, and economics, among others. Most existing work on NMVIs focuses on the asymptotic convergence of algorithms proposed to solve these problems. In this paper, we tackle the problems of exponential and fixed-time stability of the solution set of a class of NMVIs for both unconstrained and constrained problems. We first present novel conditions guaranteeing exponential stability of solutions to unconstrained NMVIs for a uniquely constructed dynamical system under mild assumptions on the gradient of the non-monotone map. Then, under similar assumptions, we construct another novel dynamical system whose equilibrium point is fixed-time stable, i.e., the trajectories reach the equilibrium within a fixed time, independent of the initial conditions. For the case of constrained NMVIs, we employ a continuous-time variant of the Korpelevich method for exponential stability of the solution set, and provide a novel scaling factor in the dynamics to achieve fixed-time stability. We illustrate the efficacy of the proposed modified dynamical systems through numerical simulations and conclude the paper with a brief note on the behavior of the discretized variant of the proposed dynamics and on further work that remains to be done.
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BibTeX
@misc{arefizadeh2026fixedtime,
title = {{On Fixed-Time Stability of Continuous Dynamics for Non-Monotone Variational Inequalities}},
author = {Sina Arefizadeh and Kunal Garg and Angelia Nedić},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.21573},
eprint = {2606.21573},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.21573},
}
RIS
TY - UNPB
TI - On Fixed-Time Stability of Continuous Dynamics for Non-Monotone Variational Inequalities
AU - Sina Arefizadeh
AU - Kunal Garg
AU - Angelia Nedić
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2606.21573
UR - https://arxiv.org/abs/2606.21573
AB - Non-monotone variational inequalities (NMVI) are an important class of problems that generalize non-convex optimization and have various applications in optimization theory, machine learning, game theory, and economics, among others. Most existing work on NMVIs focuses on the asymptotic convergence of algorithms proposed to solve these problems. In this paper, we tackle the problems of exponential and fixed-time stability of the solution set of a class of NMVIs for both unconstrained and constrained problems. We first present novel conditions guaranteeing exponential stability of solutions to unconstrained NMVIs for a uniquely constructed dynamical system under mild assumptions on the gradient of the non-monotone map. Then, under similar assumptions, we construct another novel dynamical system whose equilibrium point is fixed-time stable, i.e., the trajectories reach the equilibrium within a fixed time, independent of the initial conditions. For the case of constrained NMVIs, we employ a continuous-time variant of the Korpelevich method for exponential stability of the solution set, and provide a novel scaling factor in the dynamics to achieve fixed-time stability. We illustrate the efficacy of the proposed modified dynamical systems through numerical simulations and conclude the paper with a brief note on the behavior of the discretized variant of the proposed dynamics and on further work that remains to be done.
ER -