{"id":"https://openalex.org/W2076038142","doi":"https://doi.org/10.1137/070696209","title":"Linear Programming Approach to Deterministic Infinite Horizon Optimal Control Problems with Discounting","display_name":"Linear Programming Approach to Deterministic Infinite Horizon Optimal Control Problems with Discounting","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W2076038142","doi":"https://doi.org/10.1137/070696209","mag":"2076038142"},"language":"en","primary_location":{"id":"doi:10.1137/070696209","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070696209","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/A5017737718","display_name":"Vladimir Gaitsgory","orcid":"https://orcid.org/0000-0002-9174-4560"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Vladimir Gaitsgory","raw_affiliation_strings":["v.gaitsgory@unisa.edu.au#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"v.gaitsgory@unisa.edu.au#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044513568","display_name":"Marc Quincampoix","orcid":"https://orcid.org/0009-0004-4223-2720"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Marc Quincampoix","raw_affiliation_strings":["marc.quincampoix@univ-brest.fr#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"marc.quincampoix@univ-brest.fr#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.9416,"has_fulltext":false,"cited_by_count":104,"citation_normalized_percentile":{"value":0.9660831,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"48","issue":"4","first_page":"2480","last_page":"2512"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9983999729156494,"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":0.9983999729156494,"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":0.982699990272522,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.9812999963760376,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8048710823059082},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.737156093120575},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.6853607296943665},{"id":"https://openalex.org/keywords/discounting","display_name":"Discounting","score":0.6112945079803467},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5818603038787842},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.5243930220603943},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.5227758288383484},{"id":"https://openalex.org/keywords/dynamic-programming","display_name":"Dynamic programming","score":0.4715060293674469},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.46870583295822144},{"id":"https://openalex.org/keywords/finite-set","display_name":"Finite set","score":0.4349222779273987},{"id":"https://openalex.org/keywords/horizon","display_name":"Horizon","score":0.4334682822227478},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13914898037910461},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.12430810928344727}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8048710823059082},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.737156093120575},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.6853607296943665},{"id":"https://openalex.org/C6177178","wikidata":"https://www.wikidata.org/wiki/Q10998070","display_name":"Discounting","level":2,"score":0.6112945079803467},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5818603038787842},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.5243930220603943},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.5227758288383484},{"id":"https://openalex.org/C37404715","wikidata":"https://www.wikidata.org/wiki/Q380679","display_name":"Dynamic programming","level":2,"score":0.4715060293674469},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.46870583295822144},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.4349222779273987},{"id":"https://openalex.org/C159176650","wikidata":"https://www.wikidata.org/wiki/Q43261","display_name":"Horizon","level":2,"score":0.4334682822227478},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13914898037910461},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.12430810928344727},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"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/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/070696209","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070696209","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.536.7835","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.536.7835","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.unisanet.unisa.edu.au/Staff/VladimirGaitsgory/Papers/Lin-Progr-Appr.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":50,"referenced_works":["https://openalex.org/W35654564","https://openalex.org/W39337161","https://openalex.org/W53296665","https://openalex.org/W261814290","https://openalex.org/W307801612","https://openalex.org/W565681979","https://openalex.org/W1481789702","https://openalex.org/W1487586009","https://openalex.org/W1507296508","https://openalex.org/W1529558080","https://openalex.org/W1535396202","https://openalex.org/W1551529843","https://openalex.org/W1558902221","https://openalex.org/W1567763844","https://openalex.org/W1585160083","https://openalex.org/W1964377184","https://openalex.org/W1964771320","https://openalex.org/W1967281297","https://openalex.org/W1976237319","https://openalex.org/W1990337648","https://openalex.org/W1994996557","https://openalex.org/W2000714860","https://openalex.org/W2002450616","https://openalex.org/W2006003117","https://openalex.org/W2009060269","https://openalex.org/W2021860001","https://openalex.org/W2028758827","https://openalex.org/W2031875106","https://openalex.org/W2032316144","https://openalex.org/W2039295495","https://openalex.org/W2054625457","https://openalex.org/W2056018340","https://openalex.org/W2056945084","https://openalex.org/W2059380444","https://openalex.org/W2062736751","https://openalex.org/W2068098627","https://openalex.org/W2079867004","https://openalex.org/W2080692658","https://openalex.org/W2082219004","https://openalex.org/W2083422443","https://openalex.org/W2086412293","https://openalex.org/W2091472813","https://openalex.org/W2094211501","https://openalex.org/W2101019468","https://openalex.org/W2133707954","https://openalex.org/W2163872159","https://openalex.org/W2484199605","https://openalex.org/W2550646430","https://openalex.org/W2596682183","https://openalex.org/W2928176981"],"related_works":["https://openalex.org/W2348852664","https://openalex.org/W4311335936","https://openalex.org/W4206316684","https://openalex.org/W2095594947","https://openalex.org/W1515431846","https://openalex.org/W2995710178","https://openalex.org/W2969865478","https://openalex.org/W3121098034","https://openalex.org/W3123359883","https://openalex.org/W2025513015"],"abstract_inverted_index":{"We":[0,35,51,76],"investigate":[1],"relationships":[2],"between":[3],"the":[4,16,37,59,71,87],"deterministic":[5],"infinite":[6,29],"time":[7],"horizon":[8],"optimal":[9,60,97],"control":[10,61],"problem":[11,38,45,62,89],"with":[12,40,104],"discounting,":[13],"in":[14,20],"which":[15],"state":[17],"trajectories":[18],"remain":[19],"a":[21,27,68,105],"given":[22],"compact":[23],"set":[24],"Y,":[25],"and":[26,46,54,65,90],"certain":[28],"dimensional":[30,84],"linear":[31],"programming":[32],"(IDLP)":[33],"problem.":[34],"introduce":[36],"dual":[39,92],"respect":[41],"to":[42],"this":[43],"IDLP":[44,88],"obtain":[47],"some":[48],"duality":[49],"results.":[50],"construct":[52],"necessary":[53],"sufficient":[55],"optimality":[56],"conditions":[57],"for":[58,93],"under":[63],"consideration,":[64],"we":[66],"give":[67],"characterization":[69],"of":[70,74,86,95],"viability":[72],"kernel":[73],"Y.":[75],"also":[77],"indicate":[78],"how":[79],"one":[80],"can":[81],"use":[82],"finite":[83],"approximations":[85],"its":[91],"construction":[94,101],"near":[96],"feedback":[98],"controls.":[99],"The":[100],"is":[102],"illustrated":[103],"numerical":[106],"example.":[107]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":10},{"year":2014,"cited_by_count":15},{"year":2013,"cited_by_count":17},{"year":2012,"cited_by_count":8}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}