{"id":"https://openalex.org/W2056200277","doi":"https://doi.org/10.1155/2014/879739","title":"Global Optimization for the Sum of Concave-Convex Ratios Problem","display_name":"Global Optimization for the Sum of Concave-Convex Ratios Problem","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2056200277","doi":"https://doi.org/10.1155/2014/879739","mag":"2056200277"},"language":"en","primary_location":{"id":"doi:10.1155/2014/879739","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2014/879739","pdf_url":"https://downloads.hindawi.com/journals/jam/2014/879739.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"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 Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/jam/2014/879739.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101471954","display_name":"Xue-Gang Zhou","orcid":"https://orcid.org/0000-0001-7425-0748"},"institutions":[{"id":"https://openalex.org/I37987034","display_name":"Guangzhou University","ror":"https://ror.org/05ar8rn06","country_code":"CN","type":"education","lineage":["https://openalex.org/I37987034"]},{"id":"https://openalex.org/I4210149618","display_name":"Guangdong University of Finance","ror":"https://ror.org/04grzdh47","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210149618"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"XueGang Zhou","raw_affiliation_strings":["Department of Applied Mathematics, Guangdong University of Finance, Guangzhou, Guangdong 510521, China","School of Mathematics and Information Science, Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong, Higher Education Institutes, Guangzhou University, Guangzhou, Guangdong 510006, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Guangdong University of Finance, Guangzhou, Guangdong 510521, China","institution_ids":["https://openalex.org/I4210149618"]},{"raw_affiliation_string":"School of Mathematics and Information Science, Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong, Higher Education Institutes, Guangzhou University, Guangzhou, Guangdong 510006, China","institution_ids":["https://openalex.org/I37987034"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5068680543","display_name":"Ji-Hui Yang","orcid":"https://orcid.org/0000-0002-8069-0261"},"institutions":[{"id":"https://openalex.org/I135836153","display_name":"Shenyang Agricultural University","ror":"https://ror.org/01n7x9n08","country_code":"CN","type":"education","lineage":["https://openalex.org/I135836153"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"JiHui Yang","raw_affiliation_strings":["College of Science, Shenyang Agricultural University, Shenyang, Liaoning 110866, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Science, Shenyang Agricultural University, Shenyang, Liaoning 110866, China","institution_ids":["https://openalex.org/I135836153"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5068680543"],"corresponding_institution_ids":["https://openalex.org/I135836153"],"apc_list":{"value":1025,"currency":"USD","value_usd":1050},"apc_paid":{"value":1025,"currency":"USD","value_usd":1050},"fwci":0.462,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.6334766,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"2014","issue":null,"first_page":"1","last_page":"10"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9998000264167786,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9955000281333923,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9936000108718872,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/mathematics","display_name":"Mathematics","score":0.6966953873634338},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6127129793167114},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.5654142498970032},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5582164525985718},{"id":"https://openalex.org/keywords/conic-optimization","display_name":"Conic optimization","score":0.557270348072052},{"id":"https://openalex.org/keywords/subderivative","display_name":"Subderivative","score":0.5418063402175903},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.5335640907287598},{"id":"https://openalex.org/keywords/linearization","display_name":"Linearization","score":0.5068863034248352},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.4814707338809967},{"id":"https://openalex.org/keywords/convex-analysis","display_name":"Convex analysis","score":0.44069045782089233},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4314765930175781},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4181223213672638},{"id":"https://openalex.org/keywords/proper-convex-function","display_name":"Proper convex function","score":0.4175414443016052},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2238774299621582},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.056359559297561646}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6966953873634338},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6127129793167114},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.5654142498970032},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5582164525985718},{"id":"https://openalex.org/C79187972","wikidata":"https://www.wikidata.org/wiki/Q2654791","display_name":"Conic optimization","level":5,"score":0.557270348072052},{"id":"https://openalex.org/C200661725","wikidata":"https://www.wikidata.org/wiki/Q289500","display_name":"Subderivative","level":4,"score":0.5418063402175903},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5335640907287598},{"id":"https://openalex.org/C11210021","wikidata":"https://www.wikidata.org/wiki/Q1520713","display_name":"Linearization","level":3,"score":0.5068863034248352},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.4814707338809967},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.44069045782089233},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4314765930175781},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4181223213672638},{"id":"https://openalex.org/C50862404","wikidata":"https://www.wikidata.org/wiki/Q3075259","display_name":"Proper convex function","level":5,"score":0.4175414443016052},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2238774299621582},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.056359559297561646},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","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},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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":4,"locations":[{"id":"doi:10.1155/2014/879739","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2014/879739","pdf_url":"https://downloads.hindawi.com/journals/jam/2014/879739.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"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 Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jam/1412177565","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jam/1412177565","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:RePEc:hin:jnljam:879739","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/JAM/2014/879739.xml","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"},{"id":"pmh:oai:doaj.org/article:92672e28985344c3a268a824d4e35804","is_oa":true,"landing_page_url":"https://doaj.org/article/92672e28985344c3a268a824d4e35804","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Applied Mathematics, Vol 2014 (2014)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2014/879739","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2014/879739","pdf_url":"https://downloads.hindawi.com/journals/jam/2014/879739.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"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 Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1037077487","display_name":null,"funder_award_id":"2012RCYJ005","funder_id":"https://openalex.org/F4320321921","funder_display_name":"Natural Science Foundation of Guangdong Province"},{"id":"https://openalex.org/G4910812228","display_name":null,"funder_award_id":"770212025","funder_id":"https://openalex.org/F4320321921","funder_display_name":"Natural Science Foundation of Guangdong Province"},{"id":"https://openalex.org/G5602295844","display_name":null,"funder_award_id":"S2013040012506","funder_id":"https://openalex.org/F4320321921","funder_display_name":"Natural Science Foundation of Guangdong Province"}],"funders":[{"id":"https://openalex.org/F4320321921","display_name":"Natural Science Foundation of Guangdong Province","ror":null},{"id":"https://openalex.org/F4320325180","display_name":"Shenyang Agricultural University","ror":"https://ror.org/01n7x9n08"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2056200277.pdf","grobid_xml":"https://content.openalex.org/works/W2056200277.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W1495367673","https://openalex.org/W1499399028","https://openalex.org/W1505348331","https://openalex.org/W1556949287","https://openalex.org/W1963562015","https://openalex.org/W1994011100","https://openalex.org/W2001761698","https://openalex.org/W2010888735","https://openalex.org/W2014571690","https://openalex.org/W2014833368","https://openalex.org/W2015249958","https://openalex.org/W2060263629","https://openalex.org/W2061454251","https://openalex.org/W2077306527","https://openalex.org/W2079186480","https://openalex.org/W3150183338"],"related_works":["https://openalex.org/W2007576447","https://openalex.org/W2026600343","https://openalex.org/W2356261519","https://openalex.org/W1978014154","https://openalex.org/W4382519084","https://openalex.org/W2388375429","https://openalex.org/W2963317235","https://openalex.org/W3131050393","https://openalex.org/W4288280867","https://openalex.org/W2051968184"],"abstract_inverted_index":{"This":[0],"paper":[1],"presents":[2],"a":[3,19,43,59,70],"branch":[4],"and":[5],"bound":[6],"algorithm":[7,55],"for":[8],"globally":[9],"solving":[10],"the":[11,24,35,66,82,85],"sum":[12],"of":[13,45,65,69,72,84],"concave-convex":[14],"ratios":[15],"problem":[16,25,32,39],"(P)":[17,26],"over":[18],"compact":[20],"convex":[21,46,73],"set.":[22],"Firstly,":[23],"is":[27,40,56],"converted":[28],"to":[29,42,58,80],"an":[30],"equivalent":[31],"(P1).":[33],"Then,":[34],"initial":[36],"nonconvex":[37],"programming":[38,47,74],"reduced":[41],"sequence":[44],"problems":[48],"by":[49,63],"utilizing":[50],"linearization":[51],"technique.":[52],"The":[53],"proposed":[54,86],"convergent":[57],"global":[60],"optimal":[61],"solution":[62],"means":[64],"subsequent":[67],"solutions":[68],"series":[71],"problems.":[75],"Some":[76],"examples":[77],"are":[78],"given":[79],"illustrate":[81],"feasibility":[83],"algorithm.":[87]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}