{"id":"https://openalex.org/W2912452729","doi":"https://doi.org/10.1137/18m1188483","title":"Lipschitz Stability in Discretized Optimal Control with Application to SQP","display_name":"Lipschitz Stability in Discretized Optimal Control with Application to SQP","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2912452729","doi":"https://doi.org/10.1137/18m1188483","mag":"2912452729"},"language":"en","primary_location":{"id":"doi:10.1137/18m1188483","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1188483","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and 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/A5083269925","display_name":"Asen L. Dontchev","orcid":"https://orcid.org/0000-0003-3160-7828"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Asen L. Dontchev","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078022728","display_name":"Ilya Kolmanovsky","orcid":"https://orcid.org/0000-0002-7225-4160"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ilya Kolmanovsky","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062048570","display_name":"Mikhail Krastanov","orcid":"https://orcid.org/0000-0001-5343-7087"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mikhail I. Krastanov","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060438410","display_name":"Marco M. Nicotra","orcid":"https://orcid.org/0000-0003-0456-9766"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Marco Nicotra","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5026250785","display_name":"Vladimir M. Veliov","orcid":"https://orcid.org/0000-0001-6737-1250"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Vladimir M. Veliov","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.3138,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.79963875,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"57","issue":"1","first_page":"468","last_page":"489"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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":0.9980999827384949,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9939000010490417,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8765701055526733},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.8285509347915649},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7543826103210449},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.7302509546279907},{"id":"https://openalex.org/keywords/bellman-equation","display_name":"Bellman equation","score":0.48236292600631714},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4518727958202362},{"id":"https://openalex.org/keywords/smoothness","display_name":"Smoothness","score":0.43372124433517456},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.4116988182067871},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.40535128116607666},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.37149107456207275}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8765701055526733},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.8285509347915649},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7543826103210449},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.7302509546279907},{"id":"https://openalex.org/C14646407","wikidata":"https://www.wikidata.org/wiki/Q1430750","display_name":"Bellman equation","level":2,"score":0.48236292600631714},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4518727958202362},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.43372124433517456},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4116988182067871},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.40535128116607666},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.37149107456207275},{"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/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/18m1188483","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1188483","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and Optimization","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/13","score":0.5600000023841858,"display_name":"Climate action"}],"awards":[{"id":"https://openalex.org/G2707037455","display_name":null,"funder_award_id":"P26640-N25","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G5933245781","display_name":null,"funder_award_id":"CMMI 1562209","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8534745015","display_name":"Stability of Generalised Equations and Variational Systems","funder_award_id":"DP160100854","funder_id":"https://openalex.org/F4320334704","funder_display_name":"Australian Research Council"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"},{"id":"https://openalex.org/F4320334704","display_name":"Australian Research Council","ror":"https://ror.org/05mmh0f86"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W1993647205","https://openalex.org/W1993847172","https://openalex.org/W2000226979","https://openalex.org/W2010533236","https://openalex.org/W2018816843","https://openalex.org/W2031291057","https://openalex.org/W2115955659","https://openalex.org/W2534284975","https://openalex.org/W2786617589"],"related_works":["https://openalex.org/W4243706127","https://openalex.org/W1859185863","https://openalex.org/W2758222473","https://openalex.org/W4307691181","https://openalex.org/W4285537323","https://openalex.org/W2964126589","https://openalex.org/W1932159282","https://openalex.org/W3016225735","https://openalex.org/W1518875602","https://openalex.org/W2017412075"],"abstract_inverted_index":{"We":[0,66],"consider":[1,68],"a":[2,13,17,43,69,101,130,183],"control":[3,7,49,60,73,186],"constrained":[4],"nonlinear":[5],"optimal":[6,48,72,185],"problem":[8,74,128,187],"under":[9],"perturbations":[10],"represented":[11],"by":[12,80],"parameter":[14],"which":[15],"is":[16,50,116],"function":[18,94],"of":[19,26,54,91,112,125,146,171,177],"time.":[20],"Our":[21],"main":[22],"assumptions":[23],"involve":[24],"smoothness":[25],"the":[27,31,35,46,55,59,63,77,82,109,113,122,126,138,144,147,161,169,172,178,189],"functions":[28],"appearing":[29,61],"in":[30,62],"integral":[32,39],"functional":[33],"and":[34,42,143,174],"state":[36],"equations,":[37],"an":[38,51,88,156],"coercivity":[40],"condition,":[41],"condition":[44],"that":[45,98,107,160],"reference":[47],"isolated":[52],"solution":[53,123],"variational":[56],"inequality":[57],"for":[58],"maximum":[64],"principle.":[65],"also":[67],"corresponding":[70],"discrete-time":[71,127],"obtained":[75],"from":[76],"continuous-time":[78],"one":[79],"applying":[81],"Euler":[83],"finite-difference":[84],"scheme.":[85],"Based":[86],"on":[87,153],"enhanced":[89],"version":[90],"Robinson's":[92],"implicit":[93],"theorem,":[95],"we":[96,158],"establish":[97],"there":[99],"exists":[100],"natural":[102],"number":[103,110],"$\\bar":[104,119],"N$":[105],"such":[106],"if":[108],"$N$":[111],"grid":[114],"points":[115],"greater":[117],"than":[118],"N$,":[120],"then":[121],"mapping":[124],"has":[129],"Lipschitz":[131,141],"continuous":[132],"single-valued":[133],"localization":[134],"with":[135,166,182],"respect":[136,167],"to":[137,168],"parameter,":[139],"whose":[140],"constant":[142],"sizes":[145],"neighborhoods":[148],"involved":[149],"do":[150],"not":[151],"depend":[152],"$N$.":[154],"As":[155],"application,":[157],"show":[159],"Newton/SQP":[162],"method":[163],"converges":[164],"uniformly":[165],"step-size":[170],"discretization":[173],"small":[175],"changes":[176],"parameter.":[179],"Numerical":[180],"experiments":[181],"satellite":[184],"illustrate":[188],"convergence":[190],"result.":[191]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":5},{"year":2020,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
