{"id":"https://openalex.org/W2008465194","doi":"https://doi.org/10.1117/12.2031822","title":"Equivalence of weak Pareto optima for multiobjective optimization problems with cone constrains","display_name":"Equivalence of weak Pareto optima for multiobjective optimization problems with cone constrains","publication_year":2013,"publication_date":"2013-07-19","ids":{"openalex":"https://openalex.org/W2008465194","doi":"https://doi.org/10.1117/12.2031822","mag":"2008465194"},"language":"en","primary_location":{"id":"doi:10.1117/12.2031822","is_oa":false,"landing_page_url":"https://doi.org/10.1117/12.2031822","pdf_url":null,"source":{"id":"https://openalex.org/S183492911","display_name":"Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE","issn_l":"0277-786X","issn":["0277-786X","1996-756X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315543","host_organization_name":"SPIE","host_organization_lineage":["https://openalex.org/P4310315543"],"host_organization_lineage_names":["SPIE"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SPIE Proceedings","raw_type":"proceedings-article"},"type":"conference-paper","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/A5102430480","display_name":"Mei Cao","orcid":null},"institutions":[{"id":"https://openalex.org/I121691239","display_name":"Beihua University","ror":"https://ror.org/013jjp941","country_code":"CN","type":"education","lineage":["https://openalex.org/I121691239"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Mei Cao","raw_affiliation_strings":["Beihua Univ. (China)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Beihua Univ. (China)","institution_ids":["https://openalex.org/I121691239"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057904713","display_name":"Xue Zhao","orcid":"https://orcid.org/0000-0001-9281-7680"},"institutions":[{"id":"https://openalex.org/I121691239","display_name":"Beihua University","ror":"https://ror.org/013jjp941","country_code":"CN","type":"education","lineage":["https://openalex.org/I121691239"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xue Zhao","raw_affiliation_strings":["Beihua Univ. (China)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Beihua Univ. (China)","institution_ids":["https://openalex.org/I121691239"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I121691239"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.10164398,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"8878","issue":null,"first_page":"88784W","last_page":"88784W"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9842000007629395,"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":0.9842000007629395,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.8475536704063416},{"id":"https://openalex.org/keywords/pareto-principle","display_name":"Pareto principle","score":0.7167499661445618},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.6975598335266113},{"id":"https://openalex.org/keywords/cone","display_name":"Cone (formal languages)","score":0.6258240938186646},{"id":"https://openalex.org/keywords/multi-objective-optimization","display_name":"Multi-objective optimization","score":0.6159542798995972},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.589081883430481},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.529233455657959},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.48852312564849854},{"id":"https://openalex.org/keywords/pareto-optimal","display_name":"Pareto optimal","score":0.47634509205818176},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3857361674308777},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3334508538246155},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.20027127861976624},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.13864147663116455},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11929726600646973}],"concepts":[{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.8475536704063416},{"id":"https://openalex.org/C137635306","wikidata":"https://www.wikidata.org/wiki/Q182667","display_name":"Pareto principle","level":2,"score":0.7167499661445618},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.6975598335266113},{"id":"https://openalex.org/C30014739","wikidata":"https://www.wikidata.org/wiki/Q5159445","display_name":"Cone (formal languages)","level":2,"score":0.6258240938186646},{"id":"https://openalex.org/C68781425","wikidata":"https://www.wikidata.org/wiki/Q2052203","display_name":"Multi-objective optimization","level":2,"score":0.6159542798995972},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.589081883430481},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.529233455657959},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.48852312564849854},{"id":"https://openalex.org/C2986314615","wikidata":"https://www.wikidata.org/wiki/Q36829","display_name":"Pareto optimal","level":3,"score":0.47634509205818176},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3857361674308777},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3334508538246155},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.20027127861976624},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.13864147663116455},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11929726600646973}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1117/12.2031822","is_oa":false,"landing_page_url":"https://doi.org/10.1117/12.2031822","pdf_url":null,"source":{"id":"https://openalex.org/S183492911","display_name":"Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE","issn_l":"0277-786X","issn":["0277-786X","1996-756X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315543","host_organization_name":"SPIE","host_organization_lineage":["https://openalex.org/P4310315543"],"host_organization_lineage_names":["SPIE"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SPIE Proceedings","raw_type":"proceedings-article"},{"id":"mag:3212084866","is_oa":false,"landing_page_url":"https://jglobal.jst.go.jp/en/detail?JGLOBAL_ID=201402226019711463","pdf_url":null,"source":{"id":"https://openalex.org/S183492911","display_name":"Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE","issn_l":"0277-786X","issn":["0277-786X","1996-756X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315543","host_organization_name":"SPIE","host_organization_lineage":["https://openalex.org/P4310315543"],"host_organization_lineage_names":["SPIE"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":"Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2073298047","https://openalex.org/W1963790170","https://openalex.org/W2090178682","https://openalex.org/W2586328217","https://openalex.org/W2033790662","https://openalex.org/W2049264236","https://openalex.org/W4241467429","https://openalex.org/W2073147994","https://openalex.org/W2130100430","https://openalex.org/W2001591765"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"a":[3],"differentiable":[4],"multiobjective":[5],"optimization":[6],"problem":[7,23,29],"with":[8],"generalized":[9],"cone":[10],"constrains":[11],"is":[12,30],"considered,":[13],"and":[14,24],"the":[15,22],"equivalence":[16],"of":[17],"weak":[18],"Pareto":[19],"solutions":[20],"for":[21,25],"its":[26],"\u03b7":[27],"\u2013approximated":[28],"established":[31],"under":[32],"suitable":[33],"conditions.":[34]},"counts_by_year":[],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}
