{"id":"https://openalex.org/W2058628606","doi":"https://doi.org/10.1109/cdc.2011.6160549","title":"Nonsmooth approximate maximum principle in optimal control","display_name":"Nonsmooth approximate maximum principle in optimal control","publication_year":2011,"publication_date":"2011-12-01","ids":{"openalex":"https://openalex.org/W2058628606","doi":"https://doi.org/10.1109/cdc.2011.6160549","mag":"2058628606"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2011.6160549","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2011.6160549","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Conference on Decision and Control and European Control Conference","raw_type":"proceedings-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/A5066241737","display_name":"Boris S. Mordukhovich","orcid":"https://orcid.org/0000-0002-6071-6049"},"institutions":[{"id":"https://openalex.org/I185443292","display_name":"Wayne State University","ror":"https://ror.org/01070mq45","country_code":"US","type":"education","lineage":["https://openalex.org/I185443292"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Boris S. Mordukhovich","raw_affiliation_strings":["Department of Mathematics, Wayne State University, Detroit, MI, USA","Department of Mathematics, Wayne State University Detroit, MI 48202, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Wayne State University, Detroit, MI, USA","institution_ids":["https://openalex.org/I185443292"]},{"raw_affiliation_string":"Department of Mathematics, Wayne State University Detroit, MI 48202, USA","institution_ids":["https://openalex.org/I185443292"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5061783447","display_name":"Ilya Shvartsman","orcid":"https://orcid.org/0009-0007-5076-4067"},"institutions":[{"id":"https://openalex.org/I130769515","display_name":"Pennsylvania State University","ror":"https://ror.org/04p491231","country_code":"US","type":"education","lineage":["https://openalex.org/I130769515"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ilya Shvartsman","raw_affiliation_strings":["Department of Mathematics and Computer Science, Penn State Harrisburg, Middletown, PA, USA","Dept. of Mathematics and Computer Science, Penn State Harrisburg, Middletown, 17057, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, Penn State Harrisburg, Middletown, PA, USA","institution_ids":["https://openalex.org/I130769515"]},{"raw_affiliation_string":"Dept. of Mathematics and Computer Science, Penn State Harrisburg, Middletown, 17057, USA","institution_ids":["https://openalex.org/I130769515"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5066241737"],"corresponding_institution_ids":["https://openalex.org/I185443292"],"apc_list":null,"apc_paid":null,"fwci":0.3138,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.59724936,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"7331","last_page":"7333"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9998999834060669,"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/T13855","display_name":"Aerospace Engineering and Control Systems","score":0.996399998664856,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9952999949455261,"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/maximum-principle","display_name":"Maximum principle","score":0.935161828994751},{"id":"https://openalex.org/keywords/pontryagins-minimum-principle","display_name":"Pontryagin's minimum principle","score":0.7934496998786926},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.776153564453125},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.6924866437911987},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6454986333847046},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6394442915916443},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5441956520080566},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.535775899887085},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5281277298927307},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4388814866542816},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4256134033203125},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.4165683388710022},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4137600362300873},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.37323397397994995},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.292525053024292},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.19415047764778137}],"concepts":[{"id":"https://openalex.org/C31010330","wikidata":"https://www.wikidata.org/wiki/Q1914255","display_name":"Maximum principle","level":3,"score":0.935161828994751},{"id":"https://openalex.org/C141803461","wikidata":"https://www.wikidata.org/wiki/Q3491629","display_name":"Pontryagin's minimum principle","level":3,"score":0.7934496998786926},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.776153564453125},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.6924866437911987},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6454986333847046},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6394442915916443},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5441956520080566},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.535775899887085},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5281277298927307},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4388814866542816},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4256134033203125},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.4165683388710022},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4137600362300873},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.37323397397994995},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.292525053024292},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.19415047764778137},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"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/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},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc.2011.6160549","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2011.6160549","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Conference on Decision and Control and European Control Conference","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":3,"referenced_works":["https://openalex.org/W1976930521","https://openalex.org/W2063397726","https://openalex.org/W2798574506"],"related_works":["https://openalex.org/W4302321938","https://openalex.org/W4292923857","https://openalex.org/W1967384683","https://openalex.org/W162218241","https://openalex.org/W2962746246","https://openalex.org/W4285534277","https://openalex.org/W4211240924","https://openalex.org/W2771042763","https://openalex.org/W2031281152","https://openalex.org/W3209004265"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3],"investigate":[4],"stability":[5],"of":[6,29],"the":[7,30],"Pontryagin":[8],"maximum":[9,33],"principle":[10,34],"with":[11,20],"respect":[12],"to":[13,37],"time":[14],"discretization":[15],"for":[16],"optimal":[17],"control":[18],"problems":[19],"convex":[21],"cost":[22],"function":[23],"and":[24],"endpoint":[25],"constraints.":[26],"A":[27],"generalization":[28],"so-called":[31],"approximate":[32],"from":[35],"smooth":[36],"nonsmooth":[38],"systems":[39],"is":[40],"obtained.":[41]},"counts_by_year":[{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}