Fast Online Algorithms for Linear Programming

In this paper, we study fast first-order algorithms that approximately solve linear programs (LPs). More specifically, we apply algorithms from online linear programming to offline LPs and derive algorithms that are free of any matrix multiplication. To further improve the applicability of the proposed methods, we propose a variable-duplication technique that achieves $\mathcal{O}(\sqrt{mn/K})$ optimality gap by copying each variable $K$ times. Moreover, we identify that online algorithms can be efficiently incorporated into a column generation framework for large-scale LPs. Finally, numerical experiments show that our proposed methods can be applied either as an approximate direct solver or as an initialization subroutine in frameworks of exact LP solving.