High-Order Reduced-Gradient Methods for Composite Variational Inequalities

Yurii Nesterov ()
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Yurii Nesterov: Université catholique de Louvain, LIDAM/CORE, Belgium

No 2024025, LIDAM Discussion Papers CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE)

Abstract: This paper can be seen as an attempt of rethinking the Extra-Gradient Philosophy for solving Variational Inequality Problems. We show that the properly defined 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.

Pages: 30
Date: 2024-10-10
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