Quantitative results on a Halpern-type proximal point algorithm
Laurentiu Leustean, Pedro Pinto
备注：
This is a preprint of an article published in Computational Optimization and Applications. The final authenticated version is available online at: https://doi.org/10.1007/s10589-021-00263-w
We apply proof mining methods to analyse a result of Boikanyo and Moroşanu on the strong convergence of a Halpern-type proximal point algorithm. As a consequence, we obtain quantitative versions of this result, providing uniform effective rates of asymptotic regularity and metastability.
Weak and strong convergence of a relaxed inertial proximal splitting algorithm for solving hierarchical equilibrium problems
National School of Applied Sciences, Sidi Mohamed Ben Abdellah University（国立应用科学学院，西迪穆罕默德·本阿卜拉大学）；Cadi Ayyad university, Faculty of Sciences Semlalia（卡迪·艾雅德大学，塞姆拉拉理学院）
Quantitative asymptotic regularity and $T$-asymptotic regularity for the inexact generalized Halpern iteration
Simion Stoilow Institute of Mathematics of the Romanian Academy（罗马尼亚科学院西蒙·斯托伊洛数学研究所）；Institute for Logic and Data Science, Bucharest（布加勒斯特逻辑与数据科学研究所）；Faculty of Mathematics and Computer Science, University of Bucharest（布加勒斯特大学数学与计算机科学学院）
Restarted Reflected Halpern Acceleration for Augmented Primal-Dual Methods
Beijing International Center for Mathematical Research, Peking University（北京大学北京国际数学研究中心）；School of Mathematical Sciences, Peking University（北京大学数学科学学院）；Alibaba US, DAMO Academy（阿里巴巴美国达摩院）
