In recent years, there has been growing interest in solving linear optimization problems – or more simply “LP” – using first-order methods in order to avoid the costly matrix factorizations of traditional methods for huge-scale LP instances. The restarted primal-dual hybrid gradient method (PDHG) – together with some heuristic techniques – has emerged as a … Read more
There has been a recent surge in development of first-order methods (FOMs) for solving huge-scale linear programming (LP) problems. The attractiveness of FOMs for LP stems in part from the fact that they avoid costly matrix factorization computation. However, the efficiency of FOMs is significantly influenced – both in theory and in practice – by … Read more
Primal-dual hybrid gradient (PDHG) is a first-order method for saddle-point problems and convex programming introduced by Chambolle and Pock. Recently, Applegate et al. analyzed the behavior of PDHG when applied to an infeasible or unbounded instance of linear programming, and in particular, showed that PDHG is able to diagnose these conditions. Their analysis hinges on … Read more