Banjac Goran, Lygeros John
Automatic Control Laboratory, ETH Zurich, Zurich, Switzerland.
Optim Lett. 2021;15(8):2719-2732. doi: 10.1007/s11590-021-01706-3. Epub 2021 Feb 4.
Banjac et al. (J Optim Theory Appl 183(2):490-519, 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.
班亚克等人（《最优化理论与应用杂志》183(2):490 - 519, 2019）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性证明。具体而言，他们表明该算法生成的连续迭代之间的差异收敛到原问题和对偶问题强不可行性的证明。他们的结果是在有限维欧几里得空间设置下针对约束集的特定结构给出的。在本文中，我们将该结果扩展到实希尔伯特空间和一般非空闭凸集。此外，我们表明应用于该问题最优性条件集的近端点算法会生成类似的不可行性证明。
