Convergence Rates of Tseng's Splitting Method and Its Acceleration Schemes for Monotone Inclusion Problem with a Sum of Hölder Continuous Operators

Abstract

The monotone inclusion problem is fundamental in applied mathematics and is closely related to a wide range of practical applications. However, existing solution methods typically require the underlying operator to be Lipschitz continuous. Recently, Hölder continuity, a weaker condition than Lipschitz continuity, has proven useful in characterizing certain real-world problems. To bridge this gap, we investigate the convergence rates of the Tseng's splitting method (a fundamental algorithm for monotone inclusion problem) and its two accelerated variants, the composite extra anchored gradient method and the symplectic composite extra gradient method, under the Hölder continuity assumption. Our numerical experiments demonstrate that the numerical performance of these algorithms aligns with their respective theoretical convergence rates.