论文标题
关于道格拉斯 - 拉赫福德的渐近行为和近近点算法的凸优化
On the Asymptotic Behavior of the Douglas-Rachford and Proximal-Point Algorithms for Convex Optimization
论文作者
论文摘要
（Banjac等，2019）的作者最近表明，道格拉斯 - 拉赫福德算法为一类凸优化问题提供了不可行的证书。特别是，他们表明，算法产生的连续迭代之间的差异会收敛到原始和双重强的不可行证书。它们的结果以有限的维度欧几里得设置和约束集的特定结构显示。在本文中，我们将结果扩展到真正的希尔伯特空间和一般的非空封闭凸组。此外，我们表明，应用于问题的最佳条件集的近端算法会产生相似的不可行证书。
The authors in (Banjac et al., 2019) recently showed that the Douglas-Rachford algorithm provides certificates of infeasibility for a class of convex optimization problems. In particular, they showed that the difference between consecutive iterates generated by the algorithm converges to certificates of primal and dual strong infeasibility. Their result was shown in a finite dimensional Euclidean setting and for a particular structure of the constraint set. In this paper, we extend the result to real Hilbert spaces and a general nonempty closed convex set. Moreover, we show that the proximal-point algorithm applied to the set of optimality conditions of the problem generates similar infeasibility certificates.
