Bartlett, P.; Li, C. J.; Wu, J.; Yu, B.

In the field of optimization, developing accelerated methods for solving minimax and fixed-point problems remains a fundamental challenge. This paper presents a novel family of dual accelerated algorithms that achieve optimal convergence rates for both minimax and fixed-point problems. By exploring new anchoring techniques and adaptive strategies, we establish a comprehensive framework that unifies and extends existing acceleration mechanisms. Our theoretical analysis demonstrates that these algorithms not only meet but often exceed the performance of state- of-the-art methods. Furthermore, we provide extensive empirical evaluations on a diverse set of benchmarks, showcasing the practical efficacy and robustness of our proposed approach. These findings open new avenues for optimization research, offering versatile tools for a wide range of applications.