Minimax Theory and its Applications 09 (2024), No. 2, 357--376
Copyright Heldermann Verlag 2024
Alternated Inertial Fixed Point Algorithms
Shin-ya Matsushita
Department of Management Science and Engineering, Akita Prefectural University, Yuri-Honjo, Akita, Japan
matsushita@akita-pu.ac.jp
We study a weakly convergent fixed point algorithm with alternated inertial step to approximate a common fixed point of a sequence of mappings of nonexpansive type in a real Hilbert space. We present convergence analysis for the proposed algorithm under mild assumptions. Then, we apply the results to iterative algorithms of type alternating projection, forward-backward and primal-dual splitting and derive some convergence results. To demonstrate the effectiveness of our proposed algorithm, we present numerical comparisons of the algorithm with the existing ones.
Keywords: Nonexpansive mapping, fixed point, alternated inertial term, weak convergence, primal-dual splitting algorithm, Hilbert space.
MSC: 47H09; 47H05, 47J25, 90C25.
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