{"id":"https://openalex.org/W1973760913","doi":"https://doi.org/10.1080/10556780500065432","title":"Armijo Newton method for convex best interpolation","display_name":"Armijo Newton method for convex best interpolation","publication_year":2005,"publication_date":"2005-11-29","ids":{"openalex":"https://openalex.org/W1973760913","doi":"https://doi.org/10.1080/10556780500065432","mag":"1973760913"},"language":"en","primary_location":{"id":"doi:10.1080/10556780500065432","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556780500065432","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Methods and Software","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/A5112621269","display_name":"Houduo Qi","orcid":"https://orcid.org/0000-0003-3481-4814"},"institutions":[{"id":"https://openalex.org/I43439940","display_name":"University of Southampton","ror":"https://ror.org/01ryk1543","country_code":"GB","type":"education","lineage":["https://openalex.org/I43439940"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Hou-Duo Qi","raw_affiliation_strings":["\n School of Mathematics, The University of Southampton, Highfield, Southampton, SO17 1BJ, UK","School of Mathematics, The University of Southampton, Highfield, Southampton SO17 1BJ, UK"],"affiliations":[{"raw_affiliation_string":"\n School of Mathematics, The University of Southampton, Highfield, Southampton, SO17 1BJ, UK","institution_ids":["https://openalex.org/I43439940"]},{"raw_affiliation_string":"School of Mathematics, The University of Southampton, Highfield, Southampton SO17 1BJ, UK","institution_ids":["https://openalex.org/I43439940"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024523994","display_name":"Xiaoqi Yang","orcid":"https://orcid.org/0000-0002-5583-4032"},"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":"Xiao-Qi Yang","raw_affiliation_strings":["\n Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong","Department of Applied Mathematics, The Hong Kong Polytechnic University Hung Hom, Kowloon, Hong Kong"],"affiliations":[{"raw_affiliation_string":"\n Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong","institution_ids":["https://openalex.org/I14243506"]},{"raw_affiliation_string":"Department of Applied Mathematics, The Hong Kong Polytechnic University Hung Hom, Kowloon, Hong Kong","institution_ids":["https://openalex.org/I14243506"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5112621269"],"corresponding_institution_ids":["https://openalex.org/I43439940"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.09587181,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"21","issue":"2","first_page":"179","last_page":"200"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9997000098228455,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9997000098228455,"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/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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.968999981880188,"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":0.7229701280593872},{"id":"https://openalex.org/keywords/newtons-method","display_name":"Newton's method","score":0.7028042078018188},{"id":"https://openalex.org/keywords/newtons-method-in-optimization","display_name":"Newton's method in optimization","score":0.6150903105735779},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.548141360282898},{"id":"https://openalex.org/keywords/hessian-matrix","display_name":"Hessian matrix","score":0.5097541213035583},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4968889057636261},{"id":"https://openalex.org/keywords/secant-method","display_name":"Secant method","score":0.4866684079170227},{"id":"https://openalex.org/keywords/quadratic-growth","display_name":"Quadratic growth","score":0.48151978850364685},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.47675997018814087},{"id":"https://openalex.org/keywords/steffensens-method","display_name":"Steffensen's method","score":0.475647896528244},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4602813124656677},{"id":"https://openalex.org/keywords/line-search","display_name":"Line search","score":0.42773494124412537},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4214862585067749},{"id":"https://openalex.org/keywords/quasi-newton-method","display_name":"Quasi-Newton method","score":0.41533344984054565},{"id":"https://openalex.org/keywords/local-convergence","display_name":"Local convergence","score":0.40520530939102173},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3751411736011505},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.17008957266807556},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.15367674827575684},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.10898172855377197},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.10404053330421448}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7229701280593872},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.7028042078018188},{"id":"https://openalex.org/C179127668","wikidata":"https://www.wikidata.org/wiki/Q17086396","display_name":"Newton's method in optimization","level":4,"score":0.6150903105735779},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.548141360282898},{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.5097541213035583},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4968889057636261},{"id":"https://openalex.org/C93926214","wikidata":"https://www.wikidata.org/wiki/Q14915286","display_name":"Secant method","level":4,"score":0.4866684079170227},{"id":"https://openalex.org/C195956108","wikidata":"https://www.wikidata.org/wiki/Q7268362","display_name":"Quadratic growth","level":2,"score":0.48151978850364685},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.47675997018814087},{"id":"https://openalex.org/C173443657","wikidata":"https://www.wikidata.org/wiki/Q7606635","display_name":"Steffensen's method","level":5,"score":0.475647896528244},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4602813124656677},{"id":"https://openalex.org/C85522705","wikidata":"https://www.wikidata.org/wiki/Q3278015","display_name":"Line search","level":3,"score":0.42773494124412537},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4214862585067749},{"id":"https://openalex.org/C114954040","wikidata":"https://www.wikidata.org/wiki/Q1476018","display_name":"Quasi-Newton method","level":4,"score":0.41533344984054565},{"id":"https://openalex.org/C117898588","wikidata":"https://www.wikidata.org/wiki/Q6664310","display_name":"Local convergence","level":3,"score":0.40520530939102173},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3751411736011505},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.17008957266807556},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.15367674827575684},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.10898172855377197},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.10404053330421448},{"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/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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","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}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1080/10556780500065432","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556780500065432","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Methods and Software","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.6.5625","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.6.5625","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.maths.unsw.edu.au/~hdqi/nsl.ps","raw_type":"text"},{"id":"pmh:oai:eprints.soton.ac.uk:54540","is_oa":false,"landing_page_url":"https://eprints.soton.ac.uk/54540/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401019","display_name":"ePrints Soton (University of Southampton)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I43439940","host_organization_name":"University of Southampton","host_organization_lineage":["https://openalex.org/I43439940"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:ira.lib.polyu.edu.hk:10397/11586","is_oa":false,"landing_page_url":"http://hdl.handle.net/10397/11586","pdf_url":null,"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":"","raw_type":"Journal/Magazine Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320334704","display_name":"Australian Research Council","ror":"https://ror.org/05mmh0f86"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1487636490","https://openalex.org/W1491846897","https://openalex.org/W1497941563","https://openalex.org/W1551360398","https://openalex.org/W1975466563","https://openalex.org/W1979152443","https://openalex.org/W1992688650","https://openalex.org/W2007632272","https://openalex.org/W2015270939","https://openalex.org/W2020084878","https://openalex.org/W2047668748","https://openalex.org/W2054489011","https://openalex.org/W2061872779","https://openalex.org/W2079278943","https://openalex.org/W2087236370","https://openalex.org/W2115410170","https://openalex.org/W2162870748","https://openalex.org/W2330756801","https://openalex.org/W3029645440","https://openalex.org/W4293775970"],"related_works":["https://openalex.org/W4297921956","https://openalex.org/W2951861326","https://openalex.org/W1985487460","https://openalex.org/W2196356369","https://openalex.org/W2124368230","https://openalex.org/W2986655728","https://openalex.org/W2349605439","https://openalex.org/W568156893","https://openalex.org/W2731844756","https://openalex.org/W3001734434"],"abstract_inverted_index":{"More":[0],"than":[1],"a":[2,75,119,128],"decade":[3],"agao,":[4],"Newton's":[5,136],"method":[6,32,43,88,137],"has":[7,20,123,161],"been":[8,22],"proposed":[9,172],"for":[10,33],"constructing":[11],"the":[12,29,41,57,61,66,82,86,94,106,168,171],"convex":[13],"best":[14],"interpolant.":[15],"Its":[16],"local":[17],"quadratic":[18],"convergence":[19,84],"only":[21],"established":[23],"recently":[24],"by":[25],"recasting":[26],"it":[27,101,159],"as":[28,148,150],"generalized":[30],"Newton":[31,42,59,62,87,107,125],"semismooth":[34],"equations.":[35],"It":[36],"still":[37],"remains":[38],"mysterious":[39],"that":[40,104],"coupled":[44],"with":[45,89,138],"line":[46,90,140],"search":[47,141],"strategies":[48],"works":[49],"practically":[50],"well":[51,149],"in":[52,80,155],"global":[53,83],"sense.":[54],"Similar":[55],"to":[56,144],"classical":[58],"method,":[60],"matrix":[63,108,126],"far":[64],"from":[65],"solution":[67],"may":[68],"be":[69,145],"singular":[70,111],"or":[71],"near":[72,110],"singular,":[73],"posing":[74],"great":[76],"deal":[77],"of":[78,85,97,170],"di#culties":[79],"proving":[81],"search.":[91],"By":[92],"employing":[93],"objective":[95],"function":[96,130],"Lagrange":[98],"dual":[99],"problem,":[100],"is":[102,109,142],"observed":[103],"whenever":[105],"at":[112],"some":[113],"point,":[114],"one":[115],"can":[116],"easily":[117],"find":[118],"nearby":[120],"point":[121],"which":[122],"well-conditioned":[124],"and":[127],"lower":[129],"value.":[131],"Based":[132],"on":[133],"this":[134],"fact,":[135],"Armijo":[139],"shown":[143],"globally":[146],"convergent":[147],"locally":[151],"quadratically":[152],"convergent.":[153],"And":[154],"an":[156],"important":[157],"case,":[158],"also":[160],"finite":[162],"termination":[163],"property.":[164],"Numerical":[165],"results":[166],"demonstrate":[167],"e#ciency":[169],"method.":[173]},"counts_by_year":[{"year":2014,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}