A convergence rate of the proximal point algorithm in Banach spaces
A convergence rate of the proximal point algorithm in Banach spaces
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DOI：
10.1080/02331934.2018.1432609
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发表时间：
2018-02
期刊：
影响因子：
2.2
通讯作者：
S. Matsushita
中科院分区：
文献类型：
--
作者：
S. Matsushita
摘要研究了求真下半连续凸函数极小值的邻近点算法(PPA)的收敛速度。在Hilbert空间中，Güler证明了当算法生成的序列强收敛于极小值时，PPA的大O比可以提高到小O。在这篇文章中，我们在没有这个假设的情况下，建立了Banach空间中PPA的Little-O率。然后应用这一结果给出了关于交替投影序列和平均投影序列收敛速度的新结果。
Abstract We consider the convergence rate of the proximal point algorithm (PPA) for finding a minimizer of proper lower semicontinuous convex functions. In the Hilbert space setting, Güler showed that the big-O rate of the PPA can be improved to little-o when the sequence generated by the algorithm converges strongly to a minimizer. In this paper, we establish little-o rate of the PPA in Banach spaces without requiring this assumption. Then we apply the result to give new results on the convergence rate for sequences of alternating and averaged projections.