In contrast to many other convex optimization classes, state-of-the-art semidefinite programming solvers are still unable to efficiently solve large-scale instances. This work aims to reduce this scalability gap by proposing a novel proximal algorithm for solving general semidefinite programming problems. The key characteristic of the proposed algorithm is to be able to exploit the low-rank property inherent to several semidefinite programming problems. Exploiting the low-rank structure provides a substantial speedup and allows the operator splitting method to efficiently scale to larger instances. As opposed to other low-rank based methods, the proposed algorithm has convergence guarantees for general semidefinite programming problems. Additionally, an open-source semidefinite programming solver called ProxSDP is made available and its implementation details are discussed. Case studies are presented in order to evaluate the performance of the proposed methodology.

与许多其他凸优化类相比，最先进的半定规划求解器仍然无法有效地求解大规模实例。这项工作旨在通过提出一种用于解决一般半定规划问题的新近端算法来缩小这种可扩展性差距。所提出算法的关键特征是能够利用几个半定规划问题固有的低秩属性。利用低秩结构提供了显着的加速，并允许运算符拆分方法有效地扩展到更大的实例。与其他基于低秩的方法相反，所提出的算法对一般半定规划问题具有收敛保证。此外，一个名为ProxSDP的开源半定编程求解器可用，并讨论其实现细节。为了评估所提出的方法的性能，提出了案例研究。