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The Douglas--Rachford Algorithm Converges Only Weakly
SIAM Journal on Control and Optimization ( IF 2.2 ) Pub Date : 2020-04-21 , DOI: 10.1137/19m1308451
Minh N. Bùi , Patrick L. Combettes

SIAM Journal on Control and Optimization, Volume 58, Issue 2, Page 1118-1120, January 2020.
We show that the weak convergence of the Douglas--Rachford algorithm for finding a zero of the sum of two maximally monotone operators cannot be improved to strong convergence. Likewise, we show that strong convergence can fail for the method of partial inverses.


中文翻译:

Douglas-Rachford算法仅收敛较弱

SIAM控制与优化杂志,第58卷,第2期,第1118-1120页,2020年1月。
我们证明,道格拉斯-拉夫福德算法的弱收敛性无法提高为找到两个最大单调算子之和的零。强烈的融合。同样,我们表明强收敛可能会导致偏逆方法失败。
更新日期:2020-04-21
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