High-Order Reduced-Gradient Methods for Composite Variational Inequalities
Optimization and Control
2023-12-05 v2
Abstract
This paper can be seen as an attempt of rethinking the {\em Extra-Gradient Philosophy} for solving Variational Inequality Problems. We show that the properly defined {\em Reduced Gradients} can be used instead for finding approximate solutions to Composite Variational Inequalities by the higher-order schemes. Our methods are optimal since their performance is proportional to the lower worst-case complexity bounds for corresponding problem classes. They enjoy the provable hot-start capabilities even being applied to minimization problems. The primal version of our schemes demonstrates a linear rate of convergence under an appropriate uniform monotonicity assumption.
Cite
@article{arxiv.2311.15154,
title = {High-Order Reduced-Gradient Methods for Composite Variational Inequalities},
author = {Yurii Nesterov},
journal= {arXiv preprint arXiv:2311.15154},
year = {2023}
}