{"id":"https://openalex.org/W2777825746","doi":"https://doi.org/10.1007/s10957-017-1204-2","title":"Exactness Property of the Exact Absolute Value Penalty Function Method for Solving Convex Nondifferentiable Interval-Valued Optimization Problems","display_name":"Exactness Property of the Exact Absolute Value Penalty Function Method for Solving Convex Nondifferentiable Interval-Valued Optimization Problems","publication_year":2017,"publication_date":"2017-12-21","ids":{"openalex":"https://openalex.org/W2777825746","doi":"https://doi.org/10.1007/s10957-017-1204-2","mag":"2777825746"},"language":"en","primary_location":{"id":"doi:10.1007/s10957-017-1204-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10957-017-1204-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10957-017-1204-2.pdf","source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Optimization Theory and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10957-017-1204-2.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5050602810","display_name":"Tadeusz Antczak","orcid":"https://orcid.org/0000-0002-2218-7668"},"institutions":[{"id":"https://openalex.org/I34250744","display_name":"University of \u0141\u00f3d\u017a","ror":"https://ror.org/05cq64r17","country_code":"PL","type":"education","lineage":["https://openalex.org/I34250744"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"T. Antczak","raw_affiliation_strings":["Faculty of Mathematics and Computer Science, University of \u0141\u00f3d\u017a, Banacha 22, 90-238, Lodz, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Computer Science, University of \u0141\u00f3d\u017a, Banacha 22, 90-238, Lodz, Poland","institution_ids":["https://openalex.org/I34250744"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5050602810"],"corresponding_institution_ids":["https://openalex.org/I34250744"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":{"value":2990,"currency":"USD","value_usd":2990},"fwci":1.2745,"has_fulltext":true,"cited_by_count":21,"citation_normalized_percentile":{"value":0.82768583,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"176","issue":"1","first_page":"205","last_page":"224"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9983000159263611,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9983000159263611,"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/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9980999827384949,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8580880165100098},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.6746140718460083},{"id":"https://openalex.org/keywords/penalty-method","display_name":"Penalty method","score":0.6636442542076111},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.6590492725372314},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5967432260513306},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.5646986961364746},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4839654266834259},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4837770164012909},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.47562578320503235},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4333626627922058},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.42341914772987366},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.41347646713256836},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1674639880657196},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.0990348756313324},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.08930346369743347}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8580880165100098},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.6746140718460083},{"id":"https://openalex.org/C6180225","wikidata":"https://www.wikidata.org/wiki/Q3411771","display_name":"Penalty method","level":2,"score":0.6636442542076111},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.6590492725372314},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5967432260513306},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.5646986961364746},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4839654266834259},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4837770164012909},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.47562578320503235},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4333626627922058},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.42341914772987366},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.41347646713256836},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1674639880657196},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0990348756313324},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.08930346369743347},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10957-017-1204-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10957-017-1204-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10957-017-1204-2.pdf","source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Optimization Theory and Applications","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:spr:joptap:v:176:y:2018:i:1:d:10.1007_s10957-017-1204-2","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10957-017-1204-2","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.1007/s10957-017-1204-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10957-017-1204-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10957-017-1204-2.pdf","source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Optimization Theory and Applications","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.6100000143051147,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2777825746.pdf","grobid_xml":"https://content.openalex.org/works/W2777825746.grobid-xml"},"referenced_works_count":46,"referenced_works":["https://openalex.org/W35636098","https://openalex.org/W111413457","https://openalex.org/W113792361","https://openalex.org/W1437599971","https://openalex.org/W1538755060","https://openalex.org/W1551360398","https://openalex.org/W1561610472","https://openalex.org/W1669104078","https://openalex.org/W1967779834","https://openalex.org/W1972073618","https://openalex.org/W1973590013","https://openalex.org/W1976086748","https://openalex.org/W2001359285","https://openalex.org/W2003211636","https://openalex.org/W2003494596","https://openalex.org/W2003644018","https://openalex.org/W2008499862","https://openalex.org/W2009054772","https://openalex.org/W2011900172","https://openalex.org/W2012465196","https://openalex.org/W2022042964","https://openalex.org/W2030129759","https://openalex.org/W2032266076","https://openalex.org/W2039110906","https://openalex.org/W2041643631","https://openalex.org/W2041782481","https://openalex.org/W2056860045","https://openalex.org/W2060924166","https://openalex.org/W2066543586","https://openalex.org/W2077658674","https://openalex.org/W2083587666","https://openalex.org/W2084623031","https://openalex.org/W2091724753","https://openalex.org/W2096840534","https://openalex.org/W2119289347","https://openalex.org/W2130755446","https://openalex.org/W2165239860","https://openalex.org/W2236509707","https://openalex.org/W2322172784","https://openalex.org/W2326636823","https://openalex.org/W2502655619","https://openalex.org/W2606733399","https://openalex.org/W2787523326","https://openalex.org/W3029645440","https://openalex.org/W3203127690","https://openalex.org/W4249667877"],"related_works":["https://openalex.org/W2013038594","https://openalex.org/W4294712460","https://openalex.org/W1964191893","https://openalex.org/W2009998384","https://openalex.org/W2589063463","https://openalex.org/W4314947455","https://openalex.org/W2173203003","https://openalex.org/W4226341650","https://openalex.org/W4225392794","https://openalex.org/W3106270855"],"abstract_inverted_index":{"In":[0],"the":[1,3,31,34,46,49,56,65,68,74,88],"paper,":[2],"classical":[4],"exact":[5,35,90],"absolute":[6,36,91],"value":[7,37,92],"function":[8,39,59,94],"method":[9,40],"is":[10,41],"used":[11],"for":[12,33,73,81],"solving":[13],"a":[14],"nondifferentiable":[15,51],"constrained":[16,52,76],"interval-valued":[17,57,77,89],"optimization":[18,53,85],"problem":[19,54,79,86],"with":[20,55,87],"both":[21],"inequality":[22],"and":[23,80],"equality":[24],"constraints.":[25],"The":[26,62],"property":[27],"of":[28,30,67,70],"exactness":[29],"penalization":[32],"penalty":[38,93],"analyzed":[42],"under":[43],"assumption":[44],"that":[45],"functions":[47],"constituting":[48],"considered":[50],"objective":[58],"are":[60,95],"convex.":[61],"conditions":[63],"guaranteeing":[64],"equivalence":[66],"sets":[69],"LU-optimal":[71],"solutions":[72],"original":[75],"extremum":[78],"its":[82],"associated":[83],"penalized":[84],"given.":[96]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3}],"updated_date":"2026-07-31T08:31:51.225901","created_date":"2025-10-10T00:00:00"}
