We develop a novel randomised block coordinate descent 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 distributed and data-driven control of 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 dual variables in our optimisation framework.
翻译:我们开发了新型的随机区块协调下游原始-二元算法,用于一组非悬浮、不规则、不规则、不规则、不规则、不规则的程序。在庆祝的Chambolle-Pock原始-二元算法和Tseng的加速近似梯度方法之间的中间,我们建立了最后一个迭代和最佳的O(1/k)美元和O(1/k)2美元复杂率的全球趋同,在Convex和强烈的交错情况下,分别以美元和O(1/k)2美元作为循环计数。受分布式和数据驱动的电力系统控制驱动,我们测试了我们方法的性能,测试了AC-OPF问题第二阶调和调。分散控制是通过分布式地点边际价格(DLMPs)实现的,这是我们优化框架中的双重变量。