Hybridizing PDHG and Interior-Point Methods

TL;DR

This paper explores a hybrid approach combining PDHG and interior-point methods to leverage the speed of first-order algorithms and the accuracy of second-order methods for large-scale linear programming.

Contribution

It introduces a novel hybrid algorithm that integrates PDHG with interior-point methods to improve efficiency and accuracy in solving large-scale LP problems.

Findings

Hybrid method achieves faster convergence than traditional interior-point methods.

The approach maintains high accuracy comparable to interior-point methods.

Significant speedup observed on large-scale linear programming benchmarks.

Abstract

The Primal-Dual Hybrid Gradient (PDHG) algorithm is a first-order method that can exploit GPUs to solve large-scale linear programming problems. The approach can often be faster than the alternatives, simplex and interior-point methods, typically at the cost of much lower accuracy. This paper looks at whether PDHG can be hybridized with an interior-point method to retain some of the speed advantages of the former while capturing the accuracy advantages of the latter.