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关于利普希茨连续算子特殊情形的合成

On compositions of special cases of Lipschitz continuous operators.

作者信息

Giselsson Pontus, Moursi Walaa M

机构信息

Department of Automatic Control, Lund University, Lund, Sweden.

Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario N2L 3G1 Canada.

出版信息

Fixed Point Theory Algorithm Sci Eng. 2021;2021(1):25. doi: 10.1186/s13663-021-00709-0. Epub 2021 Dec 20.

DOI:10.1186/s13663-021-00709-0
PMID:34993526
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC8685197/
Abstract

Many iterative optimization algorithms involve compositions of special cases of Lipschitz continuous operators, namely firmly nonexpansive, averaged, and nonexpansive operators. The structure and properties of the compositions are of particular importance in the proofs of convergence of such algorithms. In this paper, we systematically study the compositions of further special cases of Lipschitz continuous operators. Applications of our results include compositions of scaled conically nonexpansive mappings, as well as the Douglas-Rachford and forward-backward operators, when applied to solve certain structured monotone inclusion and optimization problems. Several examples illustrate and tighten our conclusions.

摘要

许多迭代优化算法涉及Lipschitz连续算子的特殊情况的复合，即强非扩张算子、平均算子和非扩张算子。这些复合的结构和性质在这类算法的收敛性证明中尤为重要。在本文中，我们系统地研究了Lipschitz连续算子的进一步特殊情况的复合。我们结果的应用包括缩放锥非扩张映射的复合，以及应用于解决某些结构化单调包含和优化问题时的Douglas-Rachford算子和前向后向算子。几个例子说明了并强化了我们的结论。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5345/8685197/18bf0f5e9700/13663_2021_709_Fig13_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5345/8685197/5300284be0c5/13663_2021_709_Fig1_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5345/8685197/d689bba44cd9/13663_2021_709_Fig2_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5345/8685197/1dd9a5e80c38/13663_2021_709_Fig3_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5345/8685197/84e783ae2fe4/13663_2021_709_Fig4_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5345/8685197/3f3b23aabbf3/13663_2021_709_Fig5_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5345/8685197/3c80c6c786f8/13663_2021_709_Fig6_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5345/8685197/9b640b5fe30c/13663_2021_709_Fig7_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5345/8685197/8130b2f869a0/13663_2021_709_Fig8_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5345/8685197/a710f67a1261/13663_2021_709_Fig9_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5345/8685197/39451d5034f8/13663_2021_709_Fig10_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5345/8685197/071aac1ce8dd/13663_2021_709_Fig11_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5345/8685197/dc07c98db859/13663_2021_709_Fig12_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5345/8685197/18bf0f5e9700/13663_2021_709_Fig13_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5345/8685197/5300284be0c5/13663_2021_709_Fig1_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5345/8685197/d689bba44cd9/13663_2021_709_Fig2_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5345/8685197/1dd9a5e80c38/13663_2021_709_Fig3_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5345/8685197/84e783ae2fe4/13663_2021_709_Fig4_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5345/8685197/3f3b23aabbf3/13663_2021_709_Fig5_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5345/8685197/3c80c6c786f8/13663_2021_709_Fig6_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5345/8685197/9b640b5fe30c/13663_2021_709_Fig7_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5345/8685197/8130b2f869a0/13663_2021_709_Fig8_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5345/8685197/a710f67a1261/13663_2021_709_Fig9_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5345/8685197/39451d5034f8/13663_2021_709_Fig10_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5345/8685197/071aac1ce8dd/13663_2021_709_Fig11_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5345/8685197/dc07c98db859/13663_2021_709_Fig12_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5345/8685197/18bf0f5e9700/13663_2021_709_Fig13_HTML.jpg

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