论文标题
随机块坐标方法对于不一致的凸优化问题
Random block coordinate methods for inconsistent convex optimisation problems
论文作者
论文摘要
我们为一类非平滑型凸面程序开发了一种新型的随机块坐标原始二重式算法。位于著名的Chambolle-Pock原始二算法和Tseng加速近端方法之间的中间位置，我们建立了最后一个迭代的全球融合，以及最佳$ O（1/K）$（1/K）$和$ O（1/K^{2}）$在Convex和convex Case $ K $ K $ K $ K $ K的复杂性率分别为$ K $ K $ K $ k $ k $ k。由于分配水平电力系统的控制的复杂性的增加，我们在AC-OPF问题的二阶锥体松弛方面测试了方法的性能。分布式控制是通过分布式位置边际价格（DLMP）实现的，在我们的优化框架中，这些分布式位置边际价格（DLMP）可获得\ Revise {AS}双变量。
We develop a novel randomised block coordinate primal-dual algorithm for a class of non-smooth ill-posed convex programs. Lying in the midway between the celebrated Chambolle-Pock primal-dual algorithm and Tseng's accelerated proximal gradient method, we establish global convergence of the last iterate as well optimal $O(1/k)$ and $O(1/k^{2})$ complexity rates in the convex and strongly convex case, respectively, $k$ being the iteration count. Motivated by the increased complexity in the control of distribution level electric power systems, we test the performance of our method on a second-order cone relaxation of an AC-OPF problem. Distributed control is achieved via the distributed locational marginal prices (DLMPs), which are obtained \revise{as} dual variables in our optimisation framework.
