{"id":"https://openalex.org/W2159503542","doi":"https://doi.org/10.1137/s1052623403420857","title":"Global Minimization of Normal Quartic Polynomials Based on Global Descent Directions","display_name":"Global Minimization of Normal Quartic Polynomials Based on Global Descent Directions","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W2159503542","doi":"https://doi.org/10.1137/s1052623403420857","mag":"2159503542"},"language":"en","primary_location":{"id":"doi:10.1137/s1052623403420857","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1052623403420857","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://ira.lib.polyu.edu.hk/bitstream/10397/4765/1/Qi_Global_minimization_normal.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5011886900","display_name":"Liqun Qi","orcid":"https://orcid.org/0000-0002-1112-5250"},"institutions":[{"id":"https://openalex.org/I14243506","display_name":"Hong Kong Polytechnic University","ror":"https://ror.org/0030zas98","country_code":"HK","type":"education","lineage":["https://openalex.org/I14243506"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Liqun Qi","raw_affiliation_strings":["Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong","institution_ids":["https://openalex.org/I14243506"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027095108","display_name":"Zhong Wan","orcid":"https://orcid.org/0000-0003-3652-2460"},"institutions":[{"id":"https://openalex.org/I16609230","display_name":"Hunan University","ror":"https://ror.org/05htk5m33","country_code":"CN","type":"education","lineage":["https://openalex.org/I16609230"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhong Wan","raw_affiliation_strings":["College of Mathematics and Econometrics, Hunan University, Changsha, China"],"affiliations":[{"raw_affiliation_string":"College of Mathematics and Econometrics, Hunan University, Changsha, China","institution_ids":["https://openalex.org/I16609230"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111761716","display_name":"Yu-Fei Yang","orcid":null},"institutions":[{"id":"https://openalex.org/I16609230","display_name":"Hunan University","ror":"https://ror.org/05htk5m33","country_code":"CN","type":"education","lineage":["https://openalex.org/I16609230"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yu-Fei Yang","raw_affiliation_strings":["College of Mathematics and Econometrics, Hunan University, Changsha, China"],"affiliations":[{"raw_affiliation_string":"College of Mathematics and Econometrics, Hunan University, Changsha, China","institution_ids":["https://openalex.org/I16609230"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5111761716"],"corresponding_institution_ids":["https://openalex.org/I16609230"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":21,"citation_normalized_percentile":{"value":0.22076336,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"15","issue":"1","first_page":"275","last_page":"302"},"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9948999881744385,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9922999739646912,"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/quartic-function","display_name":"Quartic function","score":0.9029141664505005},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.849183976650238},{"id":"https://openalex.org/keywords/saddle-point","display_name":"Saddle point","score":0.6445022225379944},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5841986536979675},{"id":"https://openalex.org/keywords/global-optimization","display_name":"Global optimization","score":0.5807656645774841},{"id":"https://openalex.org/keywords/descent-direction","display_name":"Descent direction","score":0.5311583280563354},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4583034813404083},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45520830154418945},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.41015881299972534},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.386380136013031},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3056420683860779},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1807960569858551},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10839992761611938},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07550445199012756}],"concepts":[{"id":"https://openalex.org/C130432447","wikidata":"https://www.wikidata.org/wiki/Q11420049","display_name":"Quartic function","level":2,"score":0.9029141664505005},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.849183976650238},{"id":"https://openalex.org/C2681867","wikidata":"https://www.wikidata.org/wiki/Q690935","display_name":"Saddle point","level":2,"score":0.6445022225379944},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5841986536979675},{"id":"https://openalex.org/C164752517","wikidata":"https://www.wikidata.org/wiki/Q5570875","display_name":"Global optimization","level":2,"score":0.5807656645774841},{"id":"https://openalex.org/C116149140","wikidata":"https://www.wikidata.org/wiki/Q2070951","display_name":"Descent direction","level":4,"score":0.5311583280563354},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4583034813404083},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45520830154418945},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.41015881299972534},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.386380136013031},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3056420683860779},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1807960569858551},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10839992761611938},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07550445199012756},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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":2,"locations":[{"id":"doi:10.1137/s1052623403420857","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1052623403420857","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"},{"id":"pmh:oai:ira.lib.polyu.edu.hk:10397/4765","is_oa":true,"landing_page_url":"http://hdl.handle.net/10397/4765","pdf_url":"http://ira.lib.polyu.edu.hk/bitstream/10397/4765/1/Qi_Global_minimization_normal.pdf","source":{"id":"https://openalex.org/S4306400205","display_name":"PolyU Institutional Research Archive (Hong Kong Polytechnic University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I14243506","host_organization_name":"Hong Kong Polytechnic University","host_organization_lineage":["https://openalex.org/I14243506"],"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":"Journal/Magazine Article"}],"best_oa_location":{"id":"pmh:oai:ira.lib.polyu.edu.hk:10397/4765","is_oa":true,"landing_page_url":"http://hdl.handle.net/10397/4765","pdf_url":"http://ira.lib.polyu.edu.hk/bitstream/10397/4765/1/Qi_Global_minimization_normal.pdf","source":{"id":"https://openalex.org/S4306400205","display_name":"PolyU Institutional Research Archive (Hong Kong Polytechnic University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I14243506","host_organization_name":"Hong Kong Polytechnic University","host_organization_lineage":["https://openalex.org/I14243506"],"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":"Journal/Magazine Article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2159503542.pdf","grobid_xml":"https://content.openalex.org/works/W2159503542.grobid-xml"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W65560571","https://openalex.org/W402691944","https://openalex.org/W1518341038","https://openalex.org/W1602307574","https://openalex.org/W1967344706","https://openalex.org/W1982283928","https://openalex.org/W1982391474","https://openalex.org/W1992302167","https://openalex.org/W1994015146","https://openalex.org/W1994899955","https://openalex.org/W2017679634","https://openalex.org/W2027312585","https://openalex.org/W2042636063","https://openalex.org/W2050875740","https://openalex.org/W2053299192","https://openalex.org/W2093151257","https://openalex.org/W2103327612","https://openalex.org/W2110549555","https://openalex.org/W2330563963","https://openalex.org/W2894871027","https://openalex.org/W2978287015","https://openalex.org/W3007791988","https://openalex.org/W3144358832","https://openalex.org/W4234426551","https://openalex.org/W4245996348","https://openalex.org/W4249151328","https://openalex.org/W4254510460"],"related_works":["https://openalex.org/W3116205321","https://openalex.org/W1989888202","https://openalex.org/W2978731891","https://openalex.org/W2378960857","https://openalex.org/W2963092340","https://openalex.org/W4292200300","https://openalex.org/W2592651140","https://openalex.org/W1982283928","https://openalex.org/W4287771441","https://openalex.org/W2324573428"],"abstract_inverted_index":{"2005-2006":[0],">":[1,5],"Academic":[2],"research:":[3],"refereed":[4,8],"Publication":[6],"in":[7],"journal":[9]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":4},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":4},{"year":2012,"cited_by_count":2}],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2025-10-10T00:00:00"}