A First Order Method for Linear Programming Parameterized by Circuit Imbalance

Richard Cole, Christoph Hertrich, Yixin Tao, László A. Végh

Abstract: Various first order approaches have been proposed in the literature to solve Linear Programming (LP) problems, recently leading to practically efficient solvers for large-scale LPs. From a theoretical perspective, linear convergence rates have been established for first order LP algorithms, despite the fact that the underlying formulations are not strongly convex. However, the convergence rate typically depends on the Hoffman constant of a large matrix that contains the constraint matrix, as well as the right hand side, cost, and capacity vectors.