ACM Seminar: Multi-step inertial Krasnoselskii-Mann algorithm for nonexpansive operators
Applied and Computational Math (ACM) Seminar
Dr. Qiaoli Dong, Associate Professor, College of Science, Civil Aviation University of China, Tianjin, China
Multi-step inertial Krasnoselskii-Mann algorithm for nonexpansive operators
In this talk I introduce a multi–step inertial Krasnoselskiiı–Mann algorithm for nonexpansive operators, for which we present an exhaustive convergence analysis by using the bounded perturbation resilience. The obtained results can be applied to construct various multi–step inertial monotone operator splitting methods, including the multi–step inertial forward–backward splitting (MiFBS), the multi–step inertial gradient–projection method (MiGPM), the multi–step inertial Douglas-Rachford splitting (MiDRS), and the multi–step inertial primal–dual splitting method (MiPDS). We present the convergence conditions for the MiFBS, which are different with the existing results. The convergence properties of the MiDRS and MiPDS are first investigated.