{"id":"https://openalex.org/W4281388825","doi":"https://doi.org/10.1007/s11075-022-01330-x","title":"Global algorithm for a class of multiplicative programs using piecewise linear approximation technique","display_name":"Global algorithm for a class of multiplicative programs using piecewise linear approximation technique","publication_year":2022,"publication_date":"2022-05-24","ids":{"openalex":"https://openalex.org/W4281388825","doi":"https://doi.org/10.1007/s11075-022-01330-x"},"language":"en","primary_location":{"id":"doi:10.1007/s11075-022-01330-x","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-022-01330-x","pdf_url":null,"source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"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":"Numerical Algorithms","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/A5026550197","display_name":"Zhisong Hou","orcid":"https://orcid.org/0000-0002-7415-7073"},"institutions":[{"id":"https://openalex.org/I149594827","display_name":"Xidian University","ror":"https://ror.org/05s92vm98","country_code":"CN","type":"education","lineage":["https://openalex.org/I149594827"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zhisong Hou","raw_affiliation_strings":["School of Computer Science and Technology, Xidian University, South Taibai Road, Xi\u2019an, 710071, Shaanxi, China","School of Computer Science and Technology, Xidian University, South Taibai Road, Xi'an, 710071, Shaanxi, China"],"affiliations":[{"raw_affiliation_string":"School of Computer Science and Technology, Xidian University, South Taibai Road, Xi\u2019an, 710071, Shaanxi, China","institution_ids":["https://openalex.org/I149594827"]},{"raw_affiliation_string":"School of Computer Science and Technology, Xidian University, South Taibai Road, Xi'an, 710071, Shaanxi, China","institution_ids":["https://openalex.org/I149594827"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101706555","display_name":"Sanyang Liu","orcid":"https://orcid.org/0000-0002-4694-0140"},"institutions":[{"id":"https://openalex.org/I149594827","display_name":"Xidian University","ror":"https://ror.org/05s92vm98","country_code":"CN","type":"education","lineage":["https://openalex.org/I149594827"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Sanyang Liu","raw_affiliation_strings":["School of Mathematics and Statistics, Xidian University, South Taibai Road, Xi\u2019an, 710071, Shaanxi, China","School of Mathematics and Statistics, Xidian University, South Taibai Road, Xi'an, 710071, Shaanxi, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Xidian University, South Taibai Road, Xi\u2019an, 710071, Shaanxi, China","institution_ids":["https://openalex.org/I149594827"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Xidian University, South Taibai Road, Xi'an, 710071, Shaanxi, China","institution_ids":["https://openalex.org/I149594827"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5026550197"],"corresponding_institution_ids":["https://openalex.org/I149594827"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":5.7439,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.97388519,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"92","issue":"2","first_page":"1063","last_page":"1082"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9993000030517578,"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":0.9993000030517578,"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/T11409","display_name":"Advanced Wireless Network Optimization","score":0.9850999712944031,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9797000288963318,"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/mathematics","display_name":"Mathematics","score":0.7564104199409485},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6617380380630493},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.622096836566925},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.5966417789459229},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.5710070729255676},{"id":"https://openalex.org/keywords/criss-cross-algorithm","display_name":"Criss-cross algorithm","score":0.5650083422660828},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.5543293356895447},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.5124819278717041},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5087776780128479},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.47020918130874634},{"id":"https://openalex.org/keywords/branch-and-bound","display_name":"Branch and bound","score":0.4565209746360779},{"id":"https://openalex.org/keywords/linear-programming-relaxation","display_name":"Linear programming relaxation","score":0.4531439244747162},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.45067834854125977},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.44378426671028137},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.43457940220832825},{"id":"https://openalex.org/keywords/linear-fractional-programming","display_name":"Linear-fractional programming","score":0.3149794936180115}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7564104199409485},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6617380380630493},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.622096836566925},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.5966417789459229},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.5710070729255676},{"id":"https://openalex.org/C52486349","wikidata":"https://www.wikidata.org/wiki/Q17006040","display_name":"Criss-cross algorithm","level":4,"score":0.5650083422660828},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.5543293356895447},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.5124819278717041},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5087776780128479},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.47020918130874634},{"id":"https://openalex.org/C93693863","wikidata":"https://www.wikidata.org/wiki/Q897659","display_name":"Branch and bound","level":2,"score":0.4565209746360779},{"id":"https://openalex.org/C25360446","wikidata":"https://www.wikidata.org/wiki/Q1512771","display_name":"Linear programming relaxation","level":3,"score":0.4531439244747162},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.45067834854125977},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.44378426671028137},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.43457940220832825},{"id":"https://openalex.org/C205658194","wikidata":"https://www.wikidata.org/wiki/Q4168281","display_name":"Linear-fractional programming","level":3,"score":0.3149794936180115},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11075-022-01330-x","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-022-01330-x","pdf_url":null,"source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"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":"Numerical Algorithms","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4939259636","display_name":null,"funder_award_id":"61877046","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":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W61717321","https://openalex.org/W1569574031","https://openalex.org/W1764434803","https://openalex.org/W1972204922","https://openalex.org/W1978293020","https://openalex.org/W1981150408","https://openalex.org/W2008444305","https://openalex.org/W2024988725","https://openalex.org/W2025321126","https://openalex.org/W2034713829","https://openalex.org/W2039338617","https://openalex.org/W2058558758","https://openalex.org/W2068030353","https://openalex.org/W2069847787","https://openalex.org/W2090208682","https://openalex.org/W2127331687","https://openalex.org/W2185733783","https://openalex.org/W2204405059","https://openalex.org/W2465899902","https://openalex.org/W2568448495","https://openalex.org/W2744494937","https://openalex.org/W2906903862","https://openalex.org/W2972203322","https://openalex.org/W3010536279","https://openalex.org/W3023474492","https://openalex.org/W3034884403","https://openalex.org/W3037338687","https://openalex.org/W3151568068","https://openalex.org/W4205854323","https://openalex.org/W4210839712","https://openalex.org/W6608442534"],"related_works":["https://openalex.org/W2007464938","https://openalex.org/W2784100870","https://openalex.org/W4205854323","https://openalex.org/W2059496069","https://openalex.org/W1972615387","https://openalex.org/W2568448495","https://openalex.org/W30140562","https://openalex.org/W2115855742","https://openalex.org/W1998488507","https://openalex.org/W3149578574"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":1}],"updated_date":"2026-03-24T08:02:53.985720","created_date":"2025-10-10T00:00:00"}
