On a type of stability of a multicriteria integer linear programming problem in the case of a monotone norm

On a type of stability of a multicriteria integer linear programming problem in the case of a monotone norm

A multicriteria integer linear programming problem with a finite number of admissible solutions is considered. The problem consists in finding the Pareto set. Lower and upper attainable estimates of the radius of strong stability of the problem are obtained in the case when the norm in the space of...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Journal of computer & systems sciences international 2007-10, Vol.46 (5), p.714-720
Hauptverfasser: Emelichev, V. A., Kuz’min, K. G.
Format: Artikel
Sprache:eng
Schlagworte:
Linear programming
Optimization
Studies
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page 720
container_issue 5
container_start_page 714
container_title Journal of computer & systems sciences international
container_volume 46
creator Emelichev, V. A.
Kuz’min, K. G.
description A multicriteria integer linear programming problem with a finite number of admissible solutions is considered. The problem consists in finding the Pareto set. Lower and upper attainable estimates of the radius of strong stability of the problem are obtained in the case when the norm in the space of solutions is arbitrary, and the norm in the criteria space is monotone. Using the Minkowski-Mahler inequality, a formula for calculating this radius is derived in the case when the Pareto set consists of a single solution. Estimates of the radius are also found in the case of the Hölder norm in the specified spaces. A class of problems is distinguished for which the radius of strong stability is infinite. As corollaries, certain results known earlier are derived. Illustrative numerical examples are also presented.[PUBLICATION ABSTRACT]
doi_str_mv 10.1134/S1064230707050048
format Article
fullrecord <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_881080138</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2416988701</sourcerecordid><originalsourceid>FETCH-LOGICAL-c272t-80b5ddf1d3bbb84b36286e10be50dfc5f2b69b11bf8463c1e66a6e809687e6103</originalsourceid><addsrcrecordid>eNplUMtOwzAQtBBIlMIHcLO4B3bj2HWPqOIlVeoBOEd2sikuiV1s99C_J1G5oT3srGY0sxrGbhHuEUX18I6gqlLAYhwJUOkzNkMpZaGkgPMRj3Qx8ZfsKqUdgFgqqGbse-O54fm4Jx46nrKxrnf5OB2GD4c-uya6TNEZ7nymLUXeO08m8n0M22iGwfnthG1Pwyjh-Yt4YxL9OQQfcvDEfYjDNbvoTJ_o5m_P2efz08fqtVhvXt5Wj-uiKRdlLjRY2bYdtsJaqysrVKkVIViS0HaN7EqrlhbRdrpSokFSyijSsFR6QQpBzNndyXd86-dAKde7cIh-jKy1RtCAQo8iPImaGFKK1NX76AYTjzVCPVVa_6tU_AL2p2mH</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>881080138</pqid></control><display><type>article</type><title>On a type of stability of a multicriteria integer linear programming problem in the case of a monotone norm</title><source>SpringerLink Journals - AutoHoldings</source><creator>Emelichev, V. A. ; Kuz’min, K. G.</creator><creatorcontrib>Emelichev, V. A. ; Kuz’min, K. G.</creatorcontrib><description>A multicriteria integer linear programming problem with a finite number of admissible solutions is considered. The problem consists in finding the Pareto set. Lower and upper attainable estimates of the radius of strong stability of the problem are obtained in the case when the norm in the space of solutions is arbitrary, and the norm in the criteria space is monotone. Using the Minkowski-Mahler inequality, a formula for calculating this radius is derived in the case when the Pareto set consists of a single solution. Estimates of the radius are also found in the case of the Hölder norm in the specified spaces. A class of problems is distinguished for which the radius of strong stability is infinite. As corollaries, certain results known earlier are derived. Illustrative numerical examples are also presented.[PUBLICATION ABSTRACT]</description><identifier>ISSN: 1064-2307</identifier><identifier>EISSN: 1555-6530</identifier><identifier>DOI: 10.1134/S1064230707050048</identifier><language>eng</language><publisher>Silver Spring: Springer Nature B.V</publisher><subject>Linear programming ; Optimization ; Studies</subject><ispartof>Journal of computer &amp; systems sciences international, 2007-10, Vol.46 (5), p.714-720</ispartof><rights>Nauka/Interperiodica 2007</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c272t-80b5ddf1d3bbb84b36286e10be50dfc5f2b69b11bf8463c1e66a6e809687e6103</citedby><cites>FETCH-LOGICAL-c272t-80b5ddf1d3bbb84b36286e10be50dfc5f2b69b11bf8463c1e66a6e809687e6103</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27923,27924</link.rule.ids></links><search><creatorcontrib>Emelichev, V. A.</creatorcontrib><creatorcontrib>Kuz’min, K. G.</creatorcontrib><title>On a type of stability of a multicriteria integer linear programming problem in the case of a monotone norm</title><title>Journal of computer &amp; systems sciences international</title><description>A multicriteria integer linear programming problem with a finite number of admissible solutions is considered. The problem consists in finding the Pareto set. Lower and upper attainable estimates of the radius of strong stability of the problem are obtained in the case when the norm in the space of solutions is arbitrary, and the norm in the criteria space is monotone. Using the Minkowski-Mahler inequality, a formula for calculating this radius is derived in the case when the Pareto set consists of a single solution. Estimates of the radius are also found in the case of the Hölder norm in the specified spaces. A class of problems is distinguished for which the radius of strong stability is infinite. As corollaries, certain results known earlier are derived. Illustrative numerical examples are also presented.[PUBLICATION ABSTRACT]</description><subject>Linear programming</subject><subject>Optimization</subject><subject>Studies</subject><issn>1064-2307</issn><issn>1555-6530</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2007</creationdate><recordtype>article</recordtype><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><recordid>eNplUMtOwzAQtBBIlMIHcLO4B3bj2HWPqOIlVeoBOEd2sikuiV1s99C_J1G5oT3srGY0sxrGbhHuEUX18I6gqlLAYhwJUOkzNkMpZaGkgPMRj3Qx8ZfsKqUdgFgqqGbse-O54fm4Jx46nrKxrnf5OB2GD4c-uya6TNEZ7nymLUXeO08m8n0M22iGwfnthG1Pwyjh-Yt4YxL9OQQfcvDEfYjDNbvoTJ_o5m_P2efz08fqtVhvXt5Wj-uiKRdlLjRY2bYdtsJaqysrVKkVIViS0HaN7EqrlhbRdrpSokFSyijSsFR6QQpBzNndyXd86-dAKde7cIh-jKy1RtCAQo8iPImaGFKK1NX76AYTjzVCPVVa_6tU_AL2p2mH</recordid><startdate>200710</startdate><enddate>200710</enddate><creator>Emelichev, V. A.</creator><creator>Kuz’min, K. G.</creator><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7SC</scope><scope>7SP</scope><scope>7WY</scope><scope>7WZ</scope><scope>7XB</scope><scope>87Z</scope><scope>8AL</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>8FL</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BEZIV</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>FRNLG</scope><scope>F~G</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K60</scope><scope>K6~</scope><scope>K7-</scope><scope>L.-</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>M0C</scope><scope>M0N</scope><scope>P5Z</scope><scope>P62</scope><scope>PQBIZ</scope><scope>PQBZA</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PYYUZ</scope><scope>Q9U</scope></search><sort><creationdate>200710</creationdate><title>On a type of stability of a multicriteria integer linear programming problem in the case of a monotone norm</title><author>Emelichev, V. A. ; Kuz’min, K. G.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c272t-80b5ddf1d3bbb84b36286e10be50dfc5f2b69b11bf8463c1e66a6e809687e6103</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2007</creationdate><topic>Linear programming</topic><topic>Optimization</topic><topic>Studies</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Emelichev, V. A.</creatorcontrib><creatorcontrib>Kuz’min, K. G.</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Computer and Information Systems Abstracts</collection><collection>Electronics &amp; Communications Abstracts</collection><collection>ABI/INFORM Collection</collection><collection>ABI/INFORM Global (PDF only)</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>ABI/INFORM Global (Alumni Edition)</collection><collection>Computing Database (Alumni Edition)</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>ABI/INFORM Collection (Alumni Edition)</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies &amp; Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Business Premium Collection</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>Business Premium Collection (Alumni)</collection><collection>ABI/INFORM Global (Corporate)</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>ProQuest Business Collection (Alumni Edition)</collection><collection>ProQuest Business Collection</collection><collection>Computer Science Database</collection><collection>ABI/INFORM Professional Advanced</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts – Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>ABI/INFORM Global</collection><collection>Computing Database</collection><collection>Advanced Technologies &amp; Aerospace Database</collection><collection>ProQuest Advanced Technologies &amp; Aerospace Collection</collection><collection>ProQuest One Business</collection><collection>ProQuest One Business (Alumni)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ABI/INFORM Collection China</collection><collection>ProQuest Central Basic</collection><jtitle>Journal of computer &amp; systems sciences international</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Emelichev, V. A.</au><au>Kuz’min, K. G.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On a type of stability of a multicriteria integer linear programming problem in the case of a monotone norm</atitle><jtitle>Journal of computer &amp; systems sciences international</jtitle><date>2007-10</date><risdate>2007</risdate><volume>46</volume><issue>5</issue><spage>714</spage><epage>720</epage><pages>714-720</pages><issn>1064-2307</issn><eissn>1555-6530</eissn><abstract>A multicriteria integer linear programming problem with a finite number of admissible solutions is considered. The problem consists in finding the Pareto set. Lower and upper attainable estimates of the radius of strong stability of the problem are obtained in the case when the norm in the space of solutions is arbitrary, and the norm in the criteria space is monotone. Using the Minkowski-Mahler inequality, a formula for calculating this radius is derived in the case when the Pareto set consists of a single solution. Estimates of the radius are also found in the case of the Hölder norm in the specified spaces. A class of problems is distinguished for which the radius of strong stability is infinite. As corollaries, certain results known earlier are derived. Illustrative numerical examples are also presented.[PUBLICATION ABSTRACT]</abstract><cop>Silver Spring</cop><pub>Springer Nature B.V</pub><doi>10.1134/S1064230707050048</doi><tpages>7</tpages></addata></record>
fulltext fulltext
identifier ISSN: 1064-2307
ispartof Journal of computer & systems sciences international, 2007-10, Vol.46 (5), p.714-720
issn 1064-2307
1555-6530
language eng
recordid cdi_proquest_journals_881080138
source SpringerLink Journals - AutoHoldings
subjects Linear programming
Optimization
Studies
title On a type of stability of a multicriteria integer linear programming problem in the case of a monotone norm
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-08T08%3A11%3A33IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=On%20a%20type%20of%20stability%20of%20a%20multicriteria%20integer%20linear%20programming%20problem%20in%20the%20case%20of%20a%20monotone%20norm&rft.jtitle=Journal%20of%20computer%20&%20systems%20sciences%20international&rft.au=Emelichev,%20V.%20A.&rft.date=2007-10&rft.volume=46&rft.issue=5&rft.spage=714&rft.epage=720&rft.pages=714-720&rft.issn=1064-2307&rft.eissn=1555-6530&rft_id=info:doi/10.1134/S1064230707050048&rft_dat=%3Cproquest_cross%3E2416988701%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=881080138&rft_id=info:pmid/&rfr_iscdi=true