Linear superiorization for infeasible linear programming

Yair Censor, Yehuda Zur

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


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.

Original languageEnglish
Title of host publicationDiscrete Optimization and Operations Research - 9th International Conference, DOOR 2016, Proceedings
EditorsMichael Khachay, Panos Pardalos, Yury Kochetov, Vladimir Beresnev, Evgeni Nurminski
PublisherSpringer Verlag
Number of pages10
ISBN (Print)9783319449135
StatePublished - 2016
Event9th International Conference on Discrete Optimization and Operations Research, DOOR 2016 - Vladivostok, Russian Federation
Duration: 19 Sep 201623 Sep 2016

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9869 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference9th International Conference on Discrete Optimization and Operations Research, DOOR 2016
Country/TerritoryRussian Federation

Bibliographical note

Publisher Copyright:
© Springer International Publishing Switzerland 2016.


  • Cimmino method
  • Feasibility-seeking
  • Infeasible linear programming
  • Perturbation resilience
  • Proximity function
  • Simultaneous projection algorithm
  • Superiorization

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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