Linear superiorization for infeasible linear programming

Yair Censor; Yehuda Zur

doi:10.1007/978-3-319-44914-2_2

Linear superiorization for infeasible linear programming

Yair Censor
, Yehuda Zur

Department of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

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 language	English
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
Publisher	Springer Verlag
Pages	15-24
Number of pages	10
ISBN (Print)	9783319449135
DOIs	https://doi.org/10.1007/978-3-319-44914-2_2
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

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	9869 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	9th International Conference on Discrete Optimization and Operations Research, DOOR 2016
Country/Territory	Russian Federation
City	Vladivostok
Period	19/09/16 → 23/09/16

Bibliographical note

Publisher Copyright:
© Springer International Publishing Switzerland 2016.

Keywords

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

Access to Document

10.1007/978-3-319-44914-2_2

Cite this

Censor, Y., & Zur, Y. (2016). Linear superiorization for infeasible linear programming. In M. Khachay, P. Pardalos, Y. Kochetov, V. Beresnev, & E. Nurminski (Eds.), Discrete Optimization and Operations Research - 9th International Conference, DOOR 2016, Proceedings (pp. 15-24). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9869 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-44914-2_2

Censor, Yair ; Zur, Yehuda. / Linear superiorization for infeasible linear programming. Discrete Optimization and Operations Research - 9th International Conference, DOOR 2016, Proceedings. editor / Michael Khachay ; Panos Pardalos ; Yury Kochetov ; Vladimir Beresnev ; Evgeni Nurminski. Springer Verlag, 2016. pp. 15-24 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "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{\textquoteright}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.",

keywords = "Cimmino method, Feasibility-seeking, Infeasible linear programming, Perturbation resilience, Proximity function, Simultaneous projection algorithm, Superiorization",

author = "Yair Censor and Yehuda Zur",

note = "Publisher Copyright: {\textcopyright} Springer International Publishing Switzerland 2016.; 9th International Conference on Discrete Optimization and Operations Research, DOOR 2016 ; Conference date: 19-09-2016 Through 23-09-2016",

year = "2016",

doi = "10.1007/978-3-319-44914-2\_2",

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series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "15--24",

editor = "Michael Khachay and Panos Pardalos and Yury Kochetov and Vladimir Beresnev and Evgeni Nurminski",

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Censor, Y & Zur, Y 2016, Linear superiorization for infeasible linear programming. in M Khachay, P Pardalos, Y Kochetov, V Beresnev & E Nurminski (eds), Discrete Optimization and Operations Research - 9th International Conference, DOOR 2016, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9869 LNCS, Springer Verlag, pp. 15-24, 9th International Conference on Discrete Optimization and Operations Research, DOOR 2016, Vladivostok, Russian Federation, 19/09/16. https://doi.org/10.1007/978-3-319-44914-2_2

Linear superiorization for infeasible linear programming. / Censor, Yair; Zur, Yehuda.
Discrete Optimization and Operations Research - 9th International Conference, DOOR 2016, Proceedings. ed. / Michael Khachay; Panos Pardalos; Yury Kochetov; Vladimir Beresnev; Evgeni Nurminski. Springer Verlag, 2016. p. 15-24 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9869 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Linear superiorization for infeasible linear programming

AU - Censor, Yair

AU - Zur, Yehuda

N1 - Publisher Copyright: © Springer International Publishing Switzerland 2016.

PY - 2016

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N2 - 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.

AB - 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.

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KW - Proximity function

KW - Simultaneous projection algorithm

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M3 - Conference contribution

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SN - 9783319449135

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 15

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BT - Discrete Optimization and Operations Research - 9th International Conference, DOOR 2016, Proceedings

A2 - Khachay, Michael

A2 - Pardalos, Panos

A2 - Kochetov, Yury

A2 - Beresnev, Vladimir

A2 - Nurminski, Evgeni

PB - Springer Verlag

T2 - 9th International Conference on Discrete Optimization and Operations Research, DOOR 2016

Y2 - 19 September 2016 through 23 September 2016

ER -

Censor Y, Zur Y. Linear superiorization for infeasible linear programming. In Khachay M, Pardalos P, Kochetov Y, Beresnev V, Nurminski E, editors, Discrete Optimization and Operations Research - 9th International Conference, DOOR 2016, Proceedings. Springer Verlag. 2016. p. 15-24. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-319-44914-2_2

Linear superiorization for infeasible linear programming

Abstract

Publication series

Conference

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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