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.
Sublinear Convergence Rates of Extragradient-Type Methods: A Survey on Classical and Recent Developments
2 Pith papers cite this work. Polarity classification is still indexing.
2
Pith papers citing it
abstract
The extragradient (EG), introduced by G. M. Korpelevich in 1976, is a well-known method to approximate solutions of saddle-point problems and their extensions such as variational inequalities and monotone inclusions. Over the years, numerous variants of EG have been proposed and studied in the literature. Recently, these methods have gained popularity due to new applications in machine learning and robust optimization. In this work, we survey the latest developments in the EG method and its variants for approximating solutions of nonlinear equations and inclusions, with a focus on the monotonicity and co-hypomonotonicity settings. We provide a unified convergence analysis for different classes of algorithms, with an emphasis on sublinear best-iterate and last-iterate convergence rates. We also discuss recent accelerated variants of EG based on both Halpern fixed-point iteration and Nesterov's accelerated techniques. Our approach uses simple arguments and basic mathematical tools to make the proofs as elementary as possible, while maintaining generality to cover a broad range of problems.
fields
math.OC 2years
2026 2representative citing papers
Analyzes convergence rates of Tseng's splitting method and two accelerated schemes for monotone inclusion problems with sum of Hölder continuous operators.
citing papers explorer
-
Convergence Analysis of the Restarted Moving-Anchored Extra-Gradient Method in the Absence of Local Lipschitz Continuity
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.
-
Convergence Rates of Tseng's Splitting Method and Its Acceleration Schemes for Monotone Inclusion Problem with a Sum of H\"older Continuous Operators
Analyzes convergence rates of Tseng's splitting method and two accelerated schemes for monotone inclusion problems with sum of Hölder continuous operators.