Linear superiorization (LinSup) considers linear programming problems but instead of attempting to solve them with linear optimization methods it employs perturbation resilient feasibility-seeking algorithms and steers them toward reduced (not necessarily minimal) target function values. The two questions that we set out to explore experimentally are: (i) does LinSup provide a feasible point whose linear target function value is lower than that obtained by running the same feasibility-seeking algorithm without superiorization under identical conditions? (ii) How does LinSup fare in comparison with the Simplex method for solving linear programming problems? Based on our computational experiments presented here, the answers to these two questions are: 'yes' and 'very well', respectively.
Bibliographical noteFunding Information:
This work was supported by Research Grant No. 2013003 of the United States-Israel Binational Science Foundation (BSF) and by Award No. 1P20183640-01A1 of the National Cancer Institute (NCI) of the National Institutes of Health (NIH).
© 2017 IOP Publishing Ltd.
- Agmon-Motzkin-Schoenberg algorithm
- Simplex algorithm
- bounded perturbation resilience
- linear programming
ASJC Scopus subject areas
- Theoretical Computer Science
- Signal Processing
- Mathematical Physics
- Computer Science Applications
- Applied Mathematics