Linear superiorization (abbreviated: LinSup) considers linear programming (LP) problems wherein the constraints as well as the objective function are linear. It allows to steer the iterates of a feasibilityseeking iterative process toward feasible points that have lower (not necessarily minimal) values of the objective function than points that would have been reached by the same feasiblity-seeking iterative process without superiorization. Using a feasibility-seeking iterative process that converges even if the linear feasible set is empty, LinSup generates an iterative sequence that converges to a point that minimizes a proximity function which measures the linear constraints violation. In addition, due to LinSup’s repeated objective function reduction steps such a point will most probably have a reduced objective function value. We present an exploratory experimental result that illustrates the behavior of LinSup on an infeasible LP problem.
|Title of host publication||Discrete Optimization and Operations Research - 9th International Conference, DOOR 2016, Proceedings|
|Editors||Michael Khachay, Panos Pardalos, Yury Kochetov, Vladimir Beresnev, Evgeni Nurminski|
|Number of pages||10|
|State||Published - 2016|
|Event||9th International Conference on Discrete Optimization and Operations Research, DOOR 2016 - Vladivostok, Russian Federation|
Duration: 19 Sep 2016 → 23 Sep 2016
|Name||Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)|
|Conference||9th International Conference on Discrete Optimization and Operations Research, DOOR 2016|
|Period||19/09/16 → 23/09/16|
Bibliographical noteFunding Information:
We thank Gabor Herman, Ming Jiang and Evgeni Nurminski for reading a previous version of the paper and sending us comments that helped improve it. This work was supported by Research Grant No. 2013003 of the United States-Israel Binational Science Foundation (BSF).
© Springer International Publishing Switzerland 2016.
- Cimmino method
- Infeasible linear programming
- Perturbation resilience
- Proximity function
- Simultaneous projection algorithm
ASJC Scopus subject areas
- Theoretical Computer Science
- Computer Science (all)