{"id":"https://openalex.org/W1987389806","doi":"https://doi.org/10.1007/s10898-012-9846-y","title":"Characterizations of the nonemptiness and compactness for solution sets of convex set-valued optimization problems","display_name":"Characterizations of the nonemptiness and compactness for solution sets of convex set-valued optimization problems","publication_year":2012,"publication_date":"2012-01-14","ids":{"openalex":"https://openalex.org/W1987389806","doi":"https://doi.org/10.1007/s10898-012-9846-y","mag":"1987389806"},"language":"en","primary_location":{"id":"doi:10.1007/s10898-012-9846-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10898-012-9846-y","pdf_url":null,"source":{"id":"https://openalex.org/S115925768","display_name":"Journal of Global Optimization","issn_l":"0925-5001","issn":["0925-5001","1573-2916"],"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 Global Optimization","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/A5028578315","display_name":"Xiaoxu Huang","orcid":"https://orcid.org/0000-0002-4635-6112"},"institutions":[{"id":"https://openalex.org/I158842170","display_name":"Chongqing University","ror":"https://ror.org/023rhb549","country_code":"CN","type":"education","lineage":["https://openalex.org/I158842170"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"X. X. Huang","raw_affiliation_strings":["School of Economics and Business Administration, Chongqing University, Chongqing, 400030, China","School of Economics and Business Administration, Chongqing University, Chongqing, China 400030#TAB#"],"affiliations":[{"raw_affiliation_string":"School of Economics and Business Administration, Chongqing University, Chongqing, 400030, China","institution_ids":["https://openalex.org/I158842170"]},{"raw_affiliation_string":"School of Economics and Business Administration, Chongqing University, Chongqing, China 400030#TAB#","institution_ids":["https://openalex.org/I158842170"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050520268","display_name":"Jen\u2010Chih Yao","orcid":"https://orcid.org/0000-0001-9041-3375"},"institutions":[{"id":"https://openalex.org/I152743029","display_name":"Kaohsiung Medical University","ror":"https://ror.org/03gk81f96","country_code":"TW","type":"education","lineage":["https://openalex.org/I152743029"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"J. C. Yao","raw_affiliation_strings":["Center for General Education, Kaohsiung Medical University, Kaohsiung, 807, Taiwan","Center for General Education, Kaohsiung Medical University, Kaohsiung, Taiwan, 807"],"affiliations":[{"raw_affiliation_string":"Center for General Education, Kaohsiung Medical University, Kaohsiung, 807, Taiwan","institution_ids":["https://openalex.org/I152743029"]},{"raw_affiliation_string":"Center for General Education, Kaohsiung Medical University, Kaohsiung, Taiwan, 807","institution_ids":["https://openalex.org/I152743029"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5028578315"],"corresponding_institution_ids":["https://openalex.org/I158842170"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2780},"apc_paid":null,"fwci":0.6959,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.70167761,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"55","issue":"3","first_page":"611","last_page":"626"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9843000173568726,"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/T12709","display_name":"Optimization and Mathematical Programming","score":0.9343000054359436,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/compact-space","display_name":"Compact space","score":0.8676662445068359},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8543045520782471},{"id":"https://openalex.org/keywords/solution-set","display_name":"Solution set","score":0.6560215353965759},{"id":"https://openalex.org/keywords/convex-set","display_name":"Convex set","score":0.5921346545219421},{"id":"https://openalex.org/keywords/vector-optimization","display_name":"Vector optimization","score":0.5916810631752014},{"id":"https://openalex.org/keywords/cone","display_name":"Cone (formal languages)","score":0.5726630091667175},{"id":"https://openalex.org/keywords/absolutely-convex-set","display_name":"Absolutely convex set","score":0.5466998815536499},{"id":"https://openalex.org/keywords/convex-cone","display_name":"Convex cone","score":0.5428670644760132},{"id":"https://openalex.org/keywords/subderivative","display_name":"Subderivative","score":0.5342167019844055},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5250356197357178},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.5236744284629822},{"id":"https://openalex.org/keywords/conic-optimization","display_name":"Conic optimization","score":0.521298885345459},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.4855656325817108},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.43404775857925415},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3976217806339264},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.28813818097114563},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1677820086479187},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07541781663894653},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0689769983291626}],"concepts":[{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.8676662445068359},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8543045520782471},{"id":"https://openalex.org/C60033838","wikidata":"https://www.wikidata.org/wiki/Q1751685","display_name":"Solution set","level":3,"score":0.6560215353965759},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.5921346545219421},{"id":"https://openalex.org/C164088818","wikidata":"https://www.wikidata.org/wiki/Q7917833","display_name":"Vector optimization","level":4,"score":0.5916810631752014},{"id":"https://openalex.org/C30014739","wikidata":"https://www.wikidata.org/wiki/Q5159445","display_name":"Cone (formal languages)","level":2,"score":0.5726630091667175},{"id":"https://openalex.org/C6018138","wikidata":"https://www.wikidata.org/wiki/Q332715","display_name":"Absolutely convex set","level":5,"score":0.5466998815536499},{"id":"https://openalex.org/C28340159","wikidata":"https://www.wikidata.org/wiki/Q2256541","display_name":"Convex cone","level":5,"score":0.5428670644760132},{"id":"https://openalex.org/C200661725","wikidata":"https://www.wikidata.org/wiki/Q289500","display_name":"Subderivative","level":4,"score":0.5342167019844055},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5250356197357178},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.5236744284629822},{"id":"https://openalex.org/C79187972","wikidata":"https://www.wikidata.org/wiki/Q2654791","display_name":"Conic optimization","level":5,"score":0.521298885345459},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.4855656325817108},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.43404775857925415},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3976217806339264},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.28813818097114563},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1677820086479187},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07541781663894653},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0689769983291626},{"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/C122357587","wikidata":"https://www.wikidata.org/wiki/Q6934508","display_name":"Multi-swarm optimization","level":3,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10898-012-9846-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10898-012-9846-y","pdf_url":null,"source":{"id":"https://openalex.org/S115925768","display_name":"Journal of Global Optimization","issn_l":"0925-5001","issn":["0925-5001","1573-2916"],"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 Global Optimization","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:spr:jglopt:v:55:y:2013:i:3:p:611-626","is_oa":false,"landing_page_url":"http://hdl.handle.net/10.1007/s10898-012-9846-y","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":40,"referenced_works":["https://openalex.org/W79719251","https://openalex.org/W113278869","https://openalex.org/W417516028","https://openalex.org/W567872570","https://openalex.org/W596285643","https://openalex.org/W633428226","https://openalex.org/W1484024929","https://openalex.org/W1491306394","https://openalex.org/W1497613316","https://openalex.org/W1540131774","https://openalex.org/W1553702074","https://openalex.org/W1966236941","https://openalex.org/W1974665512","https://openalex.org/W1990023680","https://openalex.org/W1998900943","https://openalex.org/W2003584206","https://openalex.org/W2005096287","https://openalex.org/W2008260609","https://openalex.org/W2011243226","https://openalex.org/W2018383858","https://openalex.org/W2022799461","https://openalex.org/W2045443599","https://openalex.org/W2046807944","https://openalex.org/W2066551529","https://openalex.org/W2069876296","https://openalex.org/W2069936656","https://openalex.org/W2074292837","https://openalex.org/W2076676994","https://openalex.org/W2083486495","https://openalex.org/W2093591383","https://openalex.org/W2317783333","https://openalex.org/W2595644070","https://openalex.org/W2802620382","https://openalex.org/W4242190958","https://openalex.org/W4249125060","https://openalex.org/W4249513058","https://openalex.org/W4249667877","https://openalex.org/W4253214256","https://openalex.org/W6600075554","https://openalex.org/W6600675297"],"related_works":["https://openalex.org/W2023004229","https://openalex.org/W4200200616","https://openalex.org/W2084832285","https://openalex.org/W2522706662","https://openalex.org/W21211370","https://openalex.org/W4233008559","https://openalex.org/W4225781824","https://openalex.org/W3047013300","https://openalex.org/W2388375429","https://openalex.org/W1987389806"],"abstract_inverted_index":null,"counts_by_year":[{"year":2019,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}