Decomposition techniques for linear programming are difficult to extend to conic optimization problems with general non-polyhedral convex cones because the conic inequalities introduce an additional nonlinear coupling between the variables. However in many applications the convex cones have a partially separable structure that allows them to be characterized in terms of simpler lower-dimensional cones. The most important example is sparse semidefinite programming with a chordal sparsity pattern. Here partial separability derives from the clique decomposition theorems that characterize positive semidefinite and positive-semidefinite-completable matrices with chordal sparsity patterns. The paper describes a decomposition method that exploits partial separability in conic linear optimization. The method is based on Spingarn's method for equality constrained convex optimization, combined with a fast interior-point method for evaluating proximal operators.
Distributed Block Coordinate Descent for Minimizing Partially Separable Functions
在这项工作中，我们提出了一个分布式随机块坐标下降法最小化一个凸函数与大量的变量/坐标。我们在假设目标函数的光滑部分是部分块可分的条件下分析了它的复杂性，并表明了可分程度直接影响复杂性。这将[Richtarik，Takac：Parallel coordinate下降法for big data optimization]中的结果扩展到分布式环境。我们首先表明，部分块可分函数承认预期的可分过逼近（ESO）相对于分布采样，计算ESO参数，然后专门的复杂性结果，从最近的文献中，一般ESO假设下举行。我们描述了几种方法来分配和同步的计算在一个集群的多核计算机，并提供有前途的计算结果。
Smooth or Separable? Sparse Block Acceleration for Entropy-Regularized Linear Programs
Moscow Independent Research Institute of Artificial Intelligence（莫斯科独立人工智能研究所）；Mohamed bin Zayed University of Artificial Intelligence（穆罕默德·本·扎耶德人工智能大学）；Lomonosov Moscow State University（莫斯科罗蒙诺索夫国立大学）；Innopolis University（因诺波利斯大学）
