Strong Convergence for the Alternating Halpern–Mann Iteration in CAT(0) Spaces
研究了CAT(0)空间中交替Halpern和Krasnoselskii-Mann迭代的强收敛性，给出了渐近正则性和亚稳定性的有效速率，并推广了前向后向和Douglas-Rachford算法的强收敛版本。
In this paper we consider, in the general context of CAT(0) spaces, an iterative schema which alternates between Halpern and Krasnoselskii-Mann style iterations. We prove, under suitable conditions, the strong convergence of this algorithm, benefi ting from ideas from the proof mining program. We give quantitative information in the form of effective rates of asymptotic regularity and of metastability (in the sense of Tao). Motivated by these results we are also able to obtain strongly convergent versions of the forward-backward and the Douglas-Rachford algorithms. Our results generalize recent work by Bot, Csetnek and Meier, and Cheval and Leustean.