{"id":"https://openalex.org/W1965299678","doi":"https://doi.org/10.1007/s10957-014-0565-z","title":"Scalarization of $$\\epsilon $$ \u03f5 -Super Efficient Solutions of Set-Valued Optimization Problems in Real Ordered Linear Spaces","display_name":"Scalarization of $$\\epsilon $$ \u03f5 -Super Efficient Solutions of Set-Valued Optimization Problems in Real Ordered Linear Spaces","publication_year":2014,"publication_date":"2014-04-14","ids":{"openalex":"https://openalex.org/W1965299678","doi":"https://doi.org/10.1007/s10957-014-0565-z","mag":"1965299678"},"language":"en","primary_location":{"id":"doi:10.1007/s10957-014-0565-z","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10957-014-0565-z","pdf_url":null,"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":null,"license_id":null,"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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5061539112","display_name":"Zhiang Zhou","orcid":"https://orcid.org/0000-0002-8054-4176"},"institutions":[{"id":"https://openalex.org/I50632499","display_name":"Chongqing University of Technology","ror":"https://ror.org/04vgbd477","country_code":"CN","type":"education","lineage":["https://openalex.org/I50632499"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhi-Ang Zhou","raw_affiliation_strings":["College of Mathematics and Statistics, Chongqing University of Technology, Chongqing, 400054, China","College of Mathematics and Statistics, Chongqing University of Technology, Chongqing, China 400054#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and Statistics, Chongqing University of Technology, Chongqing, 400054, China","institution_ids":["https://openalex.org/I50632499"]},{"raw_affiliation_string":"College of Mathematics and Statistics, Chongqing University of Technology, Chongqing, China 400054#TAB#","institution_ids":["https://openalex.org/I50632499"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100549553","display_name":"Xinmin Yang","orcid":null},"institutions":[{"id":"https://openalex.org/I126924076","display_name":"Chongqing Normal University","ror":"https://ror.org/01dcw5w74","country_code":"CN","type":"education","lineage":["https://openalex.org/I126924076"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xin-Min Yang","raw_affiliation_strings":["School of Mathematics, Chongqing Normal University, Chongqing, 400047, China","School of Mathematics, Chongqing Normal University, Chongqing, China 400047#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Chongqing Normal University, Chongqing, 400047, China","institution_ids":["https://openalex.org/I126924076"]},{"raw_affiliation_string":"School of Mathematics, Chongqing Normal University, Chongqing, China 400047#TAB#","institution_ids":["https://openalex.org/I126924076"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100549553"],"corresponding_institution_ids":["https://openalex.org/I126924076"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":0.7343,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.70550665,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"162","issue":"2","first_page":"680","last_page":"693"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9997000098228455,"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":0.9997000098228455,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9934999942779541,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.9002161026000977},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.7153602838516235},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.6467903256416321},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.5355878472328186},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5317952036857605},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.47843649983406067},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.44605568051338196},{"id":"https://openalex.org/keywords/cone","display_name":"Cone (formal languages)","score":0.44500306248664856},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.42770740389823914},{"id":"https://openalex.org/keywords/decomposition-theorem","display_name":"Decomposition theorem","score":0.422306627035141},{"id":"https://openalex.org/keywords/solution-set","display_name":"Solution set","score":0.41696658730506897},{"id":"https://openalex.org/keywords/vector-optimization","display_name":"Vector optimization","score":0.4156169593334198},{"id":"https://openalex.org/keywords/danskins-theorem","display_name":"Danskin's theorem","score":0.4152313470840454},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.39677804708480835},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37790292501449585},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.377741277217865},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.36951014399528503},{"id":"https://openalex.org/keywords/brouwer-fixed-point-theorem","display_name":"Brouwer fixed-point theorem","score":0.31023645401000977},{"id":"https://openalex.org/keywords/fixed-point-theorem","display_name":"Fixed-point theorem","score":0.2525573968887329},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.14855867624282837},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06083020567893982}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9002161026000977},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.7153602838516235},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.6467903256416321},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.5355878472328186},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5317952036857605},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.47843649983406067},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44605568051338196},{"id":"https://openalex.org/C30014739","wikidata":"https://www.wikidata.org/wiki/Q5159445","display_name":"Cone (formal languages)","level":2,"score":0.44500306248664856},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.42770740389823914},{"id":"https://openalex.org/C2779182943","wikidata":"https://www.wikidata.org/wiki/Q25345219","display_name":"Decomposition theorem","level":2,"score":0.422306627035141},{"id":"https://openalex.org/C60033838","wikidata":"https://www.wikidata.org/wiki/Q1751685","display_name":"Solution set","level":3,"score":0.41696658730506897},{"id":"https://openalex.org/C164088818","wikidata":"https://www.wikidata.org/wiki/Q7917833","display_name":"Vector optimization","level":4,"score":0.4156169593334198},{"id":"https://openalex.org/C48540410","wikidata":"https://www.wikidata.org/wiki/Q5221089","display_name":"Danskin's theorem","level":4,"score":0.4152313470840454},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.39677804708480835},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37790292501449585},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.377741277217865},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.36951014399528503},{"id":"https://openalex.org/C146147875","wikidata":"https://www.wikidata.org/wiki/Q1144897","display_name":"Brouwer fixed-point theorem","level":3,"score":0.31023645401000977},{"id":"https://openalex.org/C45962547","wikidata":"https://www.wikidata.org/wiki/Q1422068","display_name":"Fixed-point theorem","level":2,"score":0.2525573968887329},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.14855867624282837},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06083020567893982},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0},{"id":"https://openalex.org/C122357587","wikidata":"https://www.wikidata.org/wiki/Q6934508","display_name":"Multi-swarm optimization","level":3,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","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},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10957-014-0565-z","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10957-014-0565-z","pdf_url":null,"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":null,"license_id":null,"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:162:y:2014:i:2:d:10.1007_s10957-014-0565-z","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10957-014-0565-z","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":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W89037727","https://openalex.org/W606402000","https://openalex.org/W1577220984","https://openalex.org/W1975718111","https://openalex.org/W1983091703","https://openalex.org/W1983898611","https://openalex.org/W2015936756","https://openalex.org/W2023949084","https://openalex.org/W2024371836","https://openalex.org/W2039165308","https://openalex.org/W2042838607","https://openalex.org/W2063012011","https://openalex.org/W2071262478","https://openalex.org/W2074909374","https://openalex.org/W2083818478","https://openalex.org/W2085855707","https://openalex.org/W2153015072","https://openalex.org/W2184280967","https://openalex.org/W2353772875","https://openalex.org/W4229824626","https://openalex.org/W4240879353"],"related_works":["https://openalex.org/W2386724422","https://openalex.org/W1988098345","https://openalex.org/W2365724145","https://openalex.org/W2355935136","https://openalex.org/W2349910014","https://openalex.org/W2381951109","https://openalex.org/W2359037450","https://openalex.org/W2051277696","https://openalex.org/W2386384165","https://openalex.org/W2078179501"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-06-19T15:47:20.252518","created_date":"2025-10-10T00:00:00"}