{"id":"https://openalex.org/W2964194415","doi":"https://doi.org/10.1007/s11590-018-1289-z","title":"Testing weak optimality of a given solution in interval linear programming revisited: NP-hardness proof, algorithm and some polynomially-solvable cases","display_name":"Testing weak optimality of a given solution in interval linear programming revisited: NP-hardness proof, algorithm and some polynomially-solvable cases","publication_year":2018,"publication_date":"2018-06-28","ids":{"openalex":"https://openalex.org/W2964194415","doi":"https://doi.org/10.1007/s11590-018-1289-z","mag":"2964194415"},"language":"en","primary_location":{"id":"doi:10.1007/s11590-018-1289-z","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11590-018-1289-z","pdf_url":null,"source":{"id":"https://openalex.org/S12647387","display_name":"Optimization Letters","issn_l":"1862-4472","issn":["1862-4472","1862-4480"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Letters","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5051556508","display_name":"Miroslav Rada","orcid":"https://orcid.org/0000-0002-1761-897X"},"institutions":[{"id":"https://openalex.org/I35913352","display_name":"Prague University of Economics and Business","ror":"https://ror.org/029ecwj92","country_code":"CZ","type":"education","lineage":["https://openalex.org/I35913352"]}],"countries":["CZ"],"is_corresponding":true,"raw_author_name":"Miroslav Rada","raw_affiliation_strings":["Department of Financial Accounting and Auditing, Faculty of Finance and Accounting, University of Economics, W. Churchill\u2019s Sq. 4, 130 67, Prague, Czech Republic","Department of Financial Accounting and Auditing, Faculty of Finance and Accounting, University of Economics, W. Churchill's Sq. 4, 130 67, Prague, Czech Republic"],"raw_orcid":"https://orcid.org/0000-0002-1761-897X","affiliations":[{"raw_affiliation_string":"Department of Financial Accounting and Auditing, Faculty of Finance and Accounting, University of Economics, W. Churchill\u2019s Sq. 4, 130 67, Prague, Czech Republic","institution_ids":["https://openalex.org/I35913352"]},{"raw_affiliation_string":"Department of Financial Accounting and Auditing, Faculty of Finance and Accounting, University of Economics, W. Churchill's Sq. 4, 130 67, Prague, Czech Republic","institution_ids":["https://openalex.org/I35913352"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081693462","display_name":"Milan Hlad\u00edk","orcid":"https://orcid.org/0000-0002-7340-8491"},"institutions":[{"id":"https://openalex.org/I21250087","display_name":"Charles University","ror":"https://ror.org/024d6js02","country_code":"CZ","type":"education","lineage":["https://openalex.org/I21250087"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Milan Hlad\u00edk","raw_affiliation_strings":["Department of Applied Mathematics, Faculty of Mathematics and Physics, Charles University, Malostransk\u00e9 n\u00e1m. 25, 118 00, Prague, Czech Republic"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Faculty of Mathematics and Physics, Charles University, Malostransk\u00e9 n\u00e1m. 25, 118 00, Prague, Czech Republic","institution_ids":["https://openalex.org/I21250087"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066790566","display_name":"Elif Garajov\u00e1","orcid":"https://orcid.org/0000-0002-3052-5970"},"institutions":[{"id":"https://openalex.org/I21250087","display_name":"Charles University","ror":"https://ror.org/024d6js02","country_code":"CZ","type":"education","lineage":["https://openalex.org/I21250087"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Elif Garajov\u00e1","raw_affiliation_strings":["Department of Applied Mathematics, Faculty of Mathematics and Physics, Charles University, Malostransk\u00e9 n\u00e1m. 25, 118 00, Prague, Czech Republic"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Faculty of Mathematics and Physics, Charles University, Malostransk\u00e9 n\u00e1m. 25, 118 00, Prague, Czech Republic","institution_ids":["https://openalex.org/I21250087"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5051556508"],"corresponding_institution_ids":["https://openalex.org/I35913352"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.6412,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.7420381,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"13","issue":"4","first_page":"875","last_page":"890"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.9944000244140625,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10969","display_name":"Water resources management and optimization","score":0.9797999858856201,"subfield":{"id":"https://openalex.org/subfields/2212","display_name":"Ocean Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/orthant","display_name":"Orthant","score":0.7742276787757874},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7698303461074829},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.6136189699172974},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.6063350439071655},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.4798709452152252},{"id":"https://openalex.org/keywords/criss-cross-algorithm","display_name":"Criss-cross algorithm","score":0.46591782569885254},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.42594847083091736},{"id":"https://openalex.org/keywords/computational-intelligence","display_name":"Computational intelligence","score":0.42377448081970215},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.41397011280059814},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.38343364000320435},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35536015033721924},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.31202226877212524},{"id":"https://openalex.org/keywords/linear-fractional-programming","display_name":"Linear-fractional programming","score":0.2970987856388092},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16221562027931213}],"concepts":[{"id":"https://openalex.org/C2780016784","wikidata":"https://www.wikidata.org/wiki/Q2714507","display_name":"Orthant","level":2,"score":0.7742276787757874},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7698303461074829},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.6136189699172974},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.6063350439071655},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4798709452152252},{"id":"https://openalex.org/C52486349","wikidata":"https://www.wikidata.org/wiki/Q17006040","display_name":"Criss-cross algorithm","level":4,"score":0.46591782569885254},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.42594847083091736},{"id":"https://openalex.org/C139502532","wikidata":"https://www.wikidata.org/wiki/Q1122090","display_name":"Computational intelligence","level":2,"score":0.42377448081970215},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.41397011280059814},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.38343364000320435},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35536015033721924},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.31202226877212524},{"id":"https://openalex.org/C205658194","wikidata":"https://www.wikidata.org/wiki/Q4168281","display_name":"Linear-fractional programming","level":3,"score":0.2970987856388092},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16221562027931213},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11590-018-1289-z","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11590-018-1289-z","pdf_url":null,"source":{"id":"https://openalex.org/S12647387","display_name":"Optimization Letters","issn_l":"1862-4472","issn":["1862-4472","1862-4480"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Letters","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5958435141","display_name":null,"funder_award_id":"18-04735S","funder_id":"https://openalex.org/F4320321006","funder_display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky"},{"id":"https://openalex.org/G6164077295","display_name":null,"funder_award_id":"156317","funder_id":"https://openalex.org/F4320309872","funder_display_name":"Grantov\u00e1 Agentura, Univerzita Karlova"},{"id":"https://openalex.org/G8248171823","display_name":null,"funder_award_id":"17-13086S","funder_id":"https://openalex.org/F4320321006","funder_display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky"}],"funders":[{"id":"https://openalex.org/F4320309872","display_name":"Grantov\u00e1 Agentura, Univerzita Karlova","ror":"https://ror.org/024d6js02"},{"id":"https://openalex.org/F4320321006","display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky","ror":"https://ror.org/01pv73b02"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W138170242","https://openalex.org/W139049954","https://openalex.org/W160117198","https://openalex.org/W754871236","https://openalex.org/W1980419470","https://openalex.org/W1981882279","https://openalex.org/W1995274880","https://openalex.org/W2009738916","https://openalex.org/W2010501361","https://openalex.org/W2035671865","https://openalex.org/W2045297403","https://openalex.org/W2059708052","https://openalex.org/W2061841834","https://openalex.org/W2074732597","https://openalex.org/W2090242866","https://openalex.org/W2151308681","https://openalex.org/W2400529723","https://openalex.org/W2538595016","https://openalex.org/W2761663315","https://openalex.org/W2788112326","https://openalex.org/W2949865709","https://openalex.org/W3105931262"],"related_works":["https://openalex.org/W4205455909","https://openalex.org/W2133667137","https://openalex.org/W4205348974","https://openalex.org/W2017494791","https://openalex.org/W2293098548","https://openalex.org/W1530516972","https://openalex.org/W2784100870","https://openalex.org/W1972615387","https://openalex.org/W2007464938","https://openalex.org/W2107423006"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2019-07-30T00:00:00"}