{"id":"https://openalex.org/W3190343043","doi":"https://doi.org/10.1137/20m1314057","title":"Convergence Rate Analysis of a Sequential Convex Programming Method with Line Search for a Class of Constrained Difference-of-Convex Optimization Problems","display_name":"Convergence Rate Analysis of a Sequential Convex Programming Method with Line Search for a Class of Constrained Difference-of-Convex Optimization Problems","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3190343043","doi":"https://doi.org/10.1137/20m1314057","mag":"3190343043"},"language":"en","primary_location":{"id":"doi:10.1137/20m1314057","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1314057","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5025532121","display_name":"Peiran Yu","orcid":"https://orcid.org/0000-0001-7245-5600"},"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":"Peiran Yu","raw_affiliation_strings":["Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong","institution_ids":["https://openalex.org/I14243506"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065214298","display_name":"Ting Kei Pong","orcid":"https://orcid.org/0000-0001-5862-2986"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ting Kei Pong","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5000609407","display_name":"Zhaosong Lu","orcid":"https://orcid.org/0000-0003-3277-7853"},"institutions":[{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zhaosong Lu","raw_affiliation_strings":["Department of Industrial and Systems Engineering, University of Minnesota, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Industrial and Systems Engineering, University of Minnesota, USA","institution_ids":["https://openalex.org/I130238516"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.8125,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.8979683,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"31","issue":"3","first_page":"2024","last_page":"2054"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9994000196456909,"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":0.9994000196456909,"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":0.9980000257492065,"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":0.9968000054359436,"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":0.7941642999649048},{"id":"https://openalex.org/keywords/line-search","display_name":"Line search","score":0.6522048115730286},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.5559308528900146},{"id":"https://openalex.org/keywords/subderivative","display_name":"Subderivative","score":0.5185080766677856},{"id":"https://openalex.org/keywords/proper-convex-function","display_name":"Proper convex function","score":0.4884568750858307},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.4847280979156494},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4789902865886688},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.47685158252716064},{"id":"https://openalex.org/keywords/nonlinear-programming","display_name":"Nonlinear programming","score":0.4666103720664978},{"id":"https://openalex.org/keywords/convex-analysis","display_name":"Convex analysis","score":0.4288649260997772},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.413524329662323},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.17515331506729126},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.15139758586883545},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12738826870918274}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7941642999649048},{"id":"https://openalex.org/C85522705","wikidata":"https://www.wikidata.org/wiki/Q3278015","display_name":"Line search","level":3,"score":0.6522048115730286},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.5559308528900146},{"id":"https://openalex.org/C200661725","wikidata":"https://www.wikidata.org/wiki/Q289500","display_name":"Subderivative","level":4,"score":0.5185080766677856},{"id":"https://openalex.org/C50862404","wikidata":"https://www.wikidata.org/wiki/Q3075259","display_name":"Proper convex function","level":5,"score":0.4884568750858307},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.4847280979156494},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4789902865886688},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.47685158252716064},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.4666103720664978},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.4288649260997772},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.413524329662323},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.17515331506729126},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.15139758586883545},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12738826870918274},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","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/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/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/20m1314057","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1314057","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:10397/90722","is_oa":false,"landing_page_url":"http://hdl.handle.net/10397/90722","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":null,"raw_type":"Journal/Magazine Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1509629106","display_name":null,"funder_award_id":"PolyU153005/17p","funder_id":"https://openalex.org/F4320321592","funder_display_name":"Research Grants Council, University Grants Committee"}],"funders":[{"id":"https://openalex.org/F4320321592","display_name":"Research Grants Council, University Grants Committee","ror":"https://ror.org/00djwmt25"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":46,"referenced_works":["https://openalex.org/W1677069601","https://openalex.org/W1855462127","https://openalex.org/W1967138577","https://openalex.org/W1973734200","https://openalex.org/W1988778152","https://openalex.org/W1993399106","https://openalex.org/W2015418199","https://openalex.org/W2021361347","https://openalex.org/W2022541060","https://openalex.org/W2027982384","https://openalex.org/W2045740595","https://openalex.org/W2072822417","https://openalex.org/W2076605490","https://openalex.org/W2078853581","https://openalex.org/W2083042020","https://openalex.org/W2089106993","https://openalex.org/W2108763700","https://openalex.org/W2112669742","https://openalex.org/W2119634512","https://openalex.org/W2126607811","https://openalex.org/W2129130711","https://openalex.org/W2129732816","https://openalex.org/W2139869783","https://openalex.org/W2170507371","https://openalex.org/W2221524898","https://openalex.org/W2225235077","https://openalex.org/W2260221836","https://openalex.org/W2265744594","https://openalex.org/W2508393166","https://openalex.org/W2535199417","https://openalex.org/W2576873436","https://openalex.org/W2741434228","https://openalex.org/W2777528688","https://openalex.org/W2784638391","https://openalex.org/W2810034112","https://openalex.org/W2929787504","https://openalex.org/W2962826994","https://openalex.org/W2963353224","https://openalex.org/W2963414688","https://openalex.org/W2963534244","https://openalex.org/W2963965252","https://openalex.org/W2964204043","https://openalex.org/W2977046017","https://openalex.org/W3013364710","https://openalex.org/W3098950028","https://openalex.org/W3100208521"],"related_works":["https://openalex.org/W2007576447","https://openalex.org/W2026600343","https://openalex.org/W2356261519","https://openalex.org/W4382519084","https://openalex.org/W1978014154","https://openalex.org/W2478309485","https://openalex.org/W4361807553","https://openalex.org/W165488893","https://openalex.org/W2040676043","https://openalex.org/W1510770274"],"abstract_inverted_index":{"In":[0],"this":[1,228],"paper,":[2],"we":[3,134,157,266],"study":[4],"the":[5,108,112,131,143,146,154,163,170,173,177,191,204,208,216,223,230,325,342],"sequential":[6],"convex":[7,121,155,192,217],"programming":[8],"method":[9],"with":[10,38,252],"monotone":[11],"line":[12],"search":[13],"(SCP$_{ls}$)":[14],"in":[15,117,130,153,190,215,329],"[Z.":[16],"Lu,":[17],"Sequential":[18],"Convex":[19],"Programming":[20],"Methods":[21],"for":[22,31,102,269],"a":[23,32,46,137,149],"Class":[24],"of":[25,34,49,111,169,176,207,233,345],"Structured":[26],"Nonlinear":[27],"Programming,":[28],"\u016dlhttps://arxiv.org/abs/1210.3039,":[29],"2012]":[30],"class":[33],"difference-of-convex":[35],"optimization":[36,104,236],"problems":[37],"multiple":[39],"smooth":[40],"inequality":[41],"constraints.":[42],"The":[43],"SCP$_{ls}$":[44,116,268],"is":[45,148,188],"representative":[47],"variant":[48],"moving-ball-approximation-type":[50],"algorithms":[51],"[A.":[52],"Auslender,":[53],"R.":[54,91,305],"Shefi,":[55],"and":[56,70,81,93,120,145,172,278,310,335],"M.":[57,94,312],"Teboulle,":[58,95],"SIAM":[59,281],"J.":[60,66,79,279,282,315],"Optim.,":[61],"20":[62],"(2010),":[63],"pp.":[64,77,89,100,287],"3232--3259;":[65],"Bolte,":[67],"Z.":[68],"Chen,":[69],"E.":[71,82,299,308],"Pauwels,":[72,83],"Math.":[73,84,96],"Program.,":[74,97],"182":[75],"(2020)":[76],"1--36;":[78],"Bolte":[80],"Oper.":[85],"Res.,":[86],"41":[87],"(2016),":[88,99,319],"442--465;":[90],"Shefi":[92],"159":[98],"137--164]":[101],"constrained":[103,235],"problems.":[105],"We":[106,198,321],"analyze":[107],"convergence":[109,343],"rate":[110],"sequence":[113],"generated":[114],"by":[115,123,294],"both":[118],"nonconvex":[119,132],"settings":[122,156,193],"imposing":[124],"suitable":[125],"Kurdyka--\u0141ojasiewicz":[126],"(KL)":[127],"assumptions.":[128,197,257],"Specifically,":[129],"settings,":[133,218],"assume":[135],"that":[136],"special":[138],"potential":[139],"function":[140,166,175,211],"related":[141],"to":[142,202,227,243,248,290,340],"objective":[144,165,171,210],"constraints":[147],"KL":[150,159,186,205,250],"function,":[151],"while":[152],"impose":[158],"assumptions":[160,187,221],"directly":[161],"on":[162,222],"extended":[164,209,231],"(i.e.,":[167],"sum":[168],"indicator":[174],"constraint":[178,224],"set).":[179],"A":[180],"relationship":[181],"between":[182],"these":[183],"two":[184],"different":[185],"established":[189],"under":[194,219,255],"additional":[195,220],"differentiability":[196],"also":[199],"discuss":[200,323],"how":[201,260,324],"deduce":[203],"exponent":[206,253],"from":[212],"its":[213],"Lagrangian":[214],"functions.":[225],"Thanks":[226],"result,":[229],"objectives":[232],"some":[234],"models":[237],"such":[238],"as":[239],"minimizing":[240,270],"$\\ell_1$":[241],"subject":[242,289],"logistic/Poisson":[244],"loss":[245],"are":[246],"found":[247],"be":[249,264,333],"functions":[251],"$\\frac12$":[254],"mild":[256],"To":[258],"illustrate":[259,341],"our":[261,330],"results":[262],"can":[263,332],"applied,":[265],"consider":[267],"$\\ell_{1-2}$":[271],"[P.":[272],"Yin,":[273],"Y.":[274],"Lou,":[275],"Q.":[276],"He,":[277],"Xin,":[280],"Sci.":[283],"Comput.,":[284],"37":[285],"(2015),":[286],"A536--A563]":[288],"residual":[291],"error":[292],"measured":[293],"$\\ell_2$":[295],"norm/Lorentzian":[296],"norm":[297],"[R.":[298],"Carrillo,":[300],"A.":[301],"B.":[302,311],"Ramirez,":[303],"G.":[304],"Arce,":[306],"K.":[307],"Barner,":[309],"Sadler,":[313],"EURASIP":[314],"Adv.":[316],"Signal":[317],"Process.":[318],"108].":[320],"first":[322],"various":[326],"conditions":[327],"required":[328],"analysis":[331],"verified,":[334],"then":[336],"perform":[337],"numerical":[338],"experiments":[339],"behaviors":[344],"SCP$_{ls}$.":[346]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":3},{"year":2020,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}