The MAEG-R method achieves convergence for monotone inclusions with merely continuous operators via a moving-anchor restart strategy, while preserving O(1/k) complexity in the Lipschitz case.
arXiv preprint arXiv:2311.15154 , year=
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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.
fields
math.OC 3years
2026 3representative citing papers
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