{"id":"https://openalex.org/W2084611946","doi":"https://doi.org/10.1155/2013/984168","title":"A Simplicial Branch and Bound Duality-Bounds Algorithm to Linear Multiplicative Programming","display_name":"A Simplicial Branch and Bound Duality-Bounds Algorithm to Linear Multiplicative Programming","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2084611946","doi":"https://doi.org/10.1155/2013/984168","mag":"2084611946"},"language":"en","primary_location":{"id":"doi:10.1155/2013/984168","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/984168","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/984168.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/2013/984168.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/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":"Xue-Gang Zhou","raw_affiliation_strings":["Department of Applied Mathematics, Guangdong University of Finance, Guangzhou, Guangdong 510521, 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"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5079293684","display_name":"Bing-Yuan Cao","orcid":"https://orcid.org/0000-0003-3589-5441"},"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"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Bing-Yuan Cao","raw_affiliation_strings":["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":"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"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5079293684"],"corresponding_institution_ids":["https://openalex.org/I37987034"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.9264,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.74497333,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"2013","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":0.9991000294685364,"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":0.9991000294685364,"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":0.9819999933242798,"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/T12709","display_name":"Optimization and Mathematical Programming","score":0.9205999970436096,"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/branch-and-bound","display_name":"Branch and bound","score":0.7287733554840088},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.6783151030540466},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.6742144823074341},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.644448459148407},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6235154271125793},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5835584402084351},{"id":"https://openalex.org/keywords/branch-and-cut","display_name":"Branch and cut","score":0.43129223585128784},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.41027602553367615},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.30958276987075806},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.05370810627937317}],"concepts":[{"id":"https://openalex.org/C93693863","wikidata":"https://www.wikidata.org/wiki/Q897659","display_name":"Branch and bound","level":2,"score":0.7287733554840088},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.6783151030540466},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.6742144823074341},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.644448459148407},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6235154271125793},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5835584402084351},{"id":"https://openalex.org/C50797617","wikidata":"https://www.wikidata.org/wiki/Q498566","display_name":"Branch and cut","level":3,"score":0.43129223585128784},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.41027602553367615},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.30958276987075806},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.05370810627937317}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2013/984168","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/984168","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/984168.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/1394807935","is_oa":false,"landing_page_url":"https://projecteuclid.org/euclid.jam/1394807935","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:984168","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/JAM/2013/984168.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:8d1159d45d8a47adb8278f3ba4947e0a","is_oa":true,"landing_page_url":"https://doaj.org/article/8d1159d45d8a47adb8278f3ba4947e0a","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 2013 (2013)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2013/984168","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/984168","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/984168.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/G6893631507","display_name":null,"funder_award_id":"70271047","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G71510864","display_name":null,"funder_award_id":"11261010","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7373144660","display_name":null,"funder_award_id":"70771030","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7851898871","display_name":null,"funder_award_id":"2012RCYJ005","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2084611946.pdf","grobid_xml":"https://content.openalex.org/works/W2084611946.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W61717321","https://openalex.org/W167138647","https://openalex.org/W1499399028","https://openalex.org/W1523445389","https://openalex.org/W1558461690","https://openalex.org/W1563945042","https://openalex.org/W1568612004","https://openalex.org/W1569574031","https://openalex.org/W1972204922","https://openalex.org/W1978293020","https://openalex.org/W1978344132","https://openalex.org/W2004203863","https://openalex.org/W2022537828","https://openalex.org/W2026971626","https://openalex.org/W2034713829","https://openalex.org/W2044670240","https://openalex.org/W2050513930","https://openalex.org/W2053060496","https://openalex.org/W2057609695","https://openalex.org/W2058469120","https://openalex.org/W2058558758","https://openalex.org/W2070501901","https://openalex.org/W2077306527","https://openalex.org/W2078340238","https://openalex.org/W2090208682","https://openalex.org/W2127331687","https://openalex.org/W2140673215","https://openalex.org/W2280657913","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W1991078291","https://openalex.org/W2084616826","https://openalex.org/W1983294952","https://openalex.org/W2009796757","https://openalex.org/W2568448495","https://openalex.org/W2008600006","https://openalex.org/W1972259521","https://openalex.org/W2024753861","https://openalex.org/W2941986668","https://openalex.org/W1997215277"],"abstract_inverted_index":{"A":[0],"simplicial":[1],"branch":[2,35],"and":[3,36],"bound":[4,37],"duality-bounds":[5],"algorithm":[6,60],"is":[7,64],"presented":[8],"to":[9,66,73,84],"globally":[10],"solving":[11,46],"the":[12,20,34,39,71,86,89],"linear":[13,48,77],"multiplicative":[14],"programming":[15,26,49,78],"(LMP).":[16],"We":[17],"firstly":[18],"convert":[19],"problem":[21],"(LMP)":[22],"into":[23],"an":[24],"equivalent":[25],"one":[27],"by":[28,45,52],"introducing<mml:math":[29],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[30],"id=\"M1\"><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:math>auxiliary":[31],"variables.":[32],"During":[33],"search,":[38],"required":[40],"lower":[41],"bounds":[42],"are":[43,82],"computed":[44],"ordinary":[47],"problems":[50],"derived":[51],"using":[53],"a":[54,67,74],"Lagrangian":[55],"duality":[56],"theory.":[57],"The":[58],"proposed":[59],"proves":[61],"that":[62],"it":[63],"convergent":[65],"global":[68],"minimum":[69],"through":[70],"solutions":[72],"series":[75],"of":[76,88],"problems.":[79],"Some":[80],"examples":[81],"given":[83],"illustrate":[85],"feasibility":[87],"present":[90],"algorithm.":[91]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}