Improved linear programming methods for checking avoiding sure loss

Nakharutai, Nawapon; Troffaes, Matthias C.M.; Caiado, Camila C.S.

Abstract

We review the simplex method and two interior-point methods (the affine scaling and the primal-dual) for solving linear programming problems for checking avoiding sure loss, and propose novel improvements. We exploit the structure of these problems to reduce their size. We also present an extra stopping criterion, and direct ways to calculate feasible starting points in almost all cases. For benchmarking, we present algorithms for generating random sets of desirable gambles that either avoid or do not avoid sure loss. We test our improvements on these linear programming methods by measuring the computational time on these generated sets. We assess the relative performance of the three methods as a function of the number of desirable gambles and the number of outcomes. Overall, the affine scaling and primal-dual methods benefit from the improvements, and they both outperform the simplex method in most scenarios. We conclude that the simplex method is not a good choice for checking avoiding sure loss. If problems are small, then there is no tangible difference in performance between all methods. For large problems, our improved primal-dual method performs at least three times faster than any of the other methods.

Citation

Nakharutai, N., Troffaes, M. C., & Caiado, C. C. (2018). Improved linear programming methods for checking avoiding sure loss. International Journal of Approximate Reasoning: Uncertainty in Intelligent Systems, 101, 293-310. https://doi.org/10.1016/j.ijar.2018.07.013

• Journal Article Type: Article
• Acceptance Date: Jul 28, 2018
• Online Publication Date: Aug 1, 2018
• Publication Date: Oct 31, 2018
• Deposit Date: Jun 15, 2018
• Publicly Available Date: Aug 1, 2019
• Journal: International Journal of Approximate Reasoning
• Print ISSN: 0888-613X
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 101
• Pages: 293-310
• DOI: https://doi.org/10.1016/j.ijar.2018.07.013
• Public URL: https://durham-repository.worktribe.com/output/1324148
• Related Public URLs: https://arxiv.org/abs/1808.03076