On practical first order methods for LP
Presenter
March 3, 2023
Abstract
Solving linear programs is nowadays an everyday task. Used even in embedded systems, but also run on very large hardware. However, solving very large models has remained a major challenge. Either because most successful algorithms require more than linear space to solve such models, or because they become extremely slow in practice.
Although the concept of first order-methods, and potential function methods have been around for a long time, they have failed to be broadly applicable, or no competitive implementations are widely available.
In this talk we will be motivating the need for such a class of algorithms, share some (known) evidence that such schemes have worked in special situations, and present results of experiments running one such algorithm (PDLP) both in standard benchmark models, and also on very large models arising from network planning. And also on a first order method for general LPs using an exponential potential function to deal with unstructured constraints.