{"id":"https://openalex.org/W2562219230","doi":"https://doi.org/10.1080/10556788.2017.1378652","title":"A limited-memory quasi-Newton algorithm for bound-constrained non-smooth optimization","display_name":"A limited-memory quasi-Newton algorithm for bound-constrained non-smooth optimization","publication_year":2017,"publication_date":"2017-10-03","ids":{"openalex":"https://openalex.org/W2562219230","doi":"https://doi.org/10.1080/10556788.2017.1378652","mag":"2562219230"},"language":"en","primary_location":{"id":"doi:10.1080/10556788.2017.1378652","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556788.2017.1378652","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/A5028709336","display_name":"Nitish Shirish Keskar","orcid":"https://orcid.org/0000-0002-2223-8496"},"institutions":[{"id":"https://openalex.org/I111979921","display_name":"Northwestern University","ror":"https://ror.org/000e0be47","country_code":"US","type":"education","lineage":["https://openalex.org/I111979921"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"N. Keskar","raw_affiliation_strings":["Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, IL 60208, USA"],"affiliations":[{"raw_affiliation_string":"Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, IL 60208, USA","institution_ids":["https://openalex.org/I111979921"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5112274231","display_name":"Andreas W\u00e4chter","orcid":null},"institutions":[{"id":"https://openalex.org/I111979921","display_name":"Northwestern University","ror":"https://ror.org/000e0be47","country_code":"US","type":"education","lineage":["https://openalex.org/I111979921"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"A. W\u00e4chter","raw_affiliation_strings":["Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, IL 60208, USA"],"affiliations":[{"raw_affiliation_string":"Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, IL 60208, USA","institution_ids":["https://openalex.org/I111979921"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5112274231"],"corresponding_institution_ids":["https://openalex.org/I111979921"],"apc_list":null,"apc_paid":null,"fwci":3.2049,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.91662685,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"34","issue":"1","first_page":"150","last_page":"171"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9980999827384949,"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":0.9980000257492065,"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/subgradient-method","display_name":"Subgradient method","score":0.7292097210884094},{"id":"https://openalex.org/keywords/line-search","display_name":"Line search","score":0.6993381977081299},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6131098866462708},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5238228440284729},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4945847690105438},{"id":"https://openalex.org/keywords/broyden\u2013fletcher\u2013goldfarb\u2013shanno-algorithm","display_name":"Broyden\u2013Fletcher\u2013Goldfarb\u2013Shanno algorithm","score":0.4497310519218445},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.448491632938385},{"id":"https://openalex.org/keywords/active-set-method","display_name":"Active set method","score":0.4335263669490814},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.42909830808639526},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.4123607575893402},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.3406021296977997},{"id":"https://openalex.org/keywords/nonlinear-programming","display_name":"Nonlinear programming","score":0.13465452194213867}],"concepts":[{"id":"https://openalex.org/C158968445","wikidata":"https://www.wikidata.org/wiki/Q7631150","display_name":"Subgradient method","level":2,"score":0.7292097210884094},{"id":"https://openalex.org/C85522705","wikidata":"https://www.wikidata.org/wiki/Q3278015","display_name":"Line search","level":3,"score":0.6993381977081299},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6131098866462708},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5238228440284729},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4945847690105438},{"id":"https://openalex.org/C132721684","wikidata":"https://www.wikidata.org/wiki/Q2877013","display_name":"Broyden\u2013Fletcher\u2013Goldfarb\u2013Shanno algorithm","level":3,"score":0.4497310519218445},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.448491632938385},{"id":"https://openalex.org/C195064452","wikidata":"https://www.wikidata.org/wiki/Q2823740","display_name":"Active set method","level":4,"score":0.4335263669490814},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42909830808639526},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4123607575893402},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.3406021296977997},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.13465452194213867},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","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/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.0},{"id":"https://openalex.org/C151319957","wikidata":"https://www.wikidata.org/wiki/Q752739","display_name":"Asynchronous communication","level":2,"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/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"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/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/10556788.2017.1378652","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556788.2017.1378652","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1980957423","display_name":null,"funder_award_id":"N00014-14-1-0313","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G2241713301","display_name":null,"funder_award_id":"DMS-1522747","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W5954235","https://openalex.org/W279731301","https://openalex.org/W875426949","https://openalex.org/W902317526","https://openalex.org/W1551360398","https://openalex.org/W1963488456","https://openalex.org/W1980223459","https://openalex.org/W1998045815","https://openalex.org/W2000359198","https://openalex.org/W2022150446","https://openalex.org/W2045581041","https://openalex.org/W2047162333","https://openalex.org/W2051434435","https://openalex.org/W2058839679","https://openalex.org/W2063670264","https://openalex.org/W2064942524","https://openalex.org/W2071634839","https://openalex.org/W2074522218","https://openalex.org/W2084788303","https://openalex.org/W2146018083","https://openalex.org/W2146292423","https://openalex.org/W2149454052","https://openalex.org/W2151568819","https://openalex.org/W2162988958","https://openalex.org/W2169988972","https://openalex.org/W2185433966","https://openalex.org/W2287259016","https://openalex.org/W2485305008","https://openalex.org/W2495560524","https://openalex.org/W2601597851","https://openalex.org/W4301014524"],"related_works":["https://openalex.org/W4289793162","https://openalex.org/W2360946740","https://openalex.org/W3093148662","https://openalex.org/W2587634790","https://openalex.org/W4385876532","https://openalex.org/W2349203978","https://openalex.org/W2761098424","https://openalex.org/W4311361601","https://openalex.org/W2166369963","https://openalex.org/W2615612939"],"abstract_inverted_index":{"We":[0,19],"consider":[1],"the":[2,25,30,38,47,56,66,70,87,92,101,106,119,135,146],"problem":[3],"of":[4,29,37,46,69,86,129,137,145],"minimizing":[5],"a":[6,35,73,127],"continuous":[7],"function":[8],"that":[9,23,54,99],"may":[10],"be":[11],"non-smooth":[12,74],"and":[13,91],"non-convex,":[14],"subject":[15],"to":[16,133],"bound":[17],"constraints.":[18],"propose":[20,77],"an":[21,50,84,95,141],"algorithm":[22],"uses":[24,94],"L-BFGS":[26],"quasi-Newton":[27],"approximation":[28,85],"problem's":[31],"curvature":[32],"together":[33],"with":[34],"variant":[36],"weak":[39],"Wolfe":[40],"line":[41],"search.":[42],"The":[43,80],"key":[44],"ingredient":[45],"method":[48],"is":[49],"active-set":[51],"selection":[52],"strategy":[53],"defines":[55],"subspace":[57],"in":[58],"which":[59],"search":[60,108],"directions":[61],"are":[62],"computed.":[63],"To":[64],"overcome":[65],"inherent":[67],"shortsightedness":[68],"gradient":[71],"for":[72,118],"function,":[75],"we":[76,122],"two":[78],"strategies.":[79],"first":[81],"relies":[82],"on":[83,105,126],"\u03b5-minimum":[88],"norm":[89],"subgradient,":[90],"second":[93],"iterative":[96],"corrective":[97],"loop":[98],"augments":[100],"active":[102],"set":[103,128],"based":[104],"resulting":[107],"directions.":[109],"While":[110],"theoretical":[111],"convergence":[112],"guarantees":[113],"have":[114],"been":[115],"elusive":[116],"even":[117],"unconstrained":[120],"case,":[121],"present":[123],"numerical":[124],"results":[125],"standard":[130],"test":[131],"problems":[132],"illustrate":[134],"efficacy":[136],"our":[138],"approach,":[139],"using":[140],"open-source":[142],"Python":[143],"implementation":[144],"proposed":[147],"algorithm.":[148]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3}],"updated_date":"2026-04-02T15:55:50.835912","created_date":"2025-10-10T00:00:00"}