Exploiting Low-Rank Structure in Semidefinite Programming by Approximate Operator Splitting. (arXiv:1810.05231v1 [math.OC])

In contrast with many other convex optimization classes, state-of-the-art semidefinite programming solvers are yet 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 proposed methodology, based on the primal-dual hybrid gradient method, allows the presence of linear inequalities without the need of adding extra slack variables and avoids solving a linear system at each iteration. More importantly, it does simultaneously compute the dual variables associated with the linear constraints. The main contribution of this work is to achieve a substantial speedup by effectively adjusting the proposed algorithm in order to exploit the low-rank property inherent to several semidefinite programming problems. This proposed modification is the key element that allows the operator splitting method to efficiently scale to larger instances. Convergence guaran 查看全文>>