Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Hybridizing PDHG and Interior-Point Methods

Edward Rothberg

TL;DR

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.

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.

Hybridizing PDHG and Interior-Point Methods

TL;DR

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.

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.
Paper Structure (14 sections, 3 equations, 2 figures, 5 tables, 1 algorithm)

This paper contains 14 sections, 3 equations, 2 figures, 5 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Background
  3. Presolve and Scaling
  4. Warm-Starting an Interior-Point Method
  5. Our Warm-Start Approach
  6. Experimental Results
  7. Testing Environment
  8. Test Models
  9. Violation Metric
  10. The Performance-Accuracy Tradeoff for Simple Variants
  11. Results for the Hybrid Approach
  12. Impact on Iteration Counts and Robustness
  13. Discussion
  14. Conclusions

Figures (2)

  • Figure 1: Runtimes and maximum violations for the models in the Mittelmann test set, for four solution approaches. Runtime ratios larger than 100 are reported as 100. Similarly, maximum violations smaller than $10^{-12}$ or larger than $10^{6}$ are reported as those values.
  • Figure 2: Runtimes and maximum violations for the models in the Mittelmann test set, for four solution approaches. Runtime ratios larger than 100 are reported as 100. Similarly, maximum violations smaller than $10^{-12}$ or larger than $10^{6}$ are reported as those values.