{"id":"https://openalex.org/W2132705050","doi":"https://doi.org/10.1080/00207160701864483","title":"An optimization problem in deregulated electricity markets solved with the nonsmooth maximum principle","display_name":"An optimization problem in deregulated electricity markets solved with the nonsmooth maximum principle","publication_year":2008,"publication_date":"2008-12-05","ids":{"openalex":"https://openalex.org/W2132705050","doi":"https://doi.org/10.1080/00207160701864483","mag":"2132705050"},"language":"en","primary_location":{"id":"doi:10.1080/00207160701864483","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160701864483","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"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":"International Journal of Computer Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://hdl.handle.net/10651/8445","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5046537826","display_name":"L. Bay\u00f3n","orcid":null},"institutions":[{"id":"https://openalex.org/I165339363","display_name":"Universidad de Oviedo","ror":"https://ror.org/006gksa02","country_code":"ES","type":"education","lineage":["https://openalex.org/I165339363"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"L. Bay\u00f3n","raw_affiliation_strings":["Department of Mathematics , University of Oviedo , Campus of Viesques, Gij\u00f3n, Spain","Department of Mathematics, University of Oviedo, Gijon, Spain#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , University of Oviedo , Campus of Viesques, Gij\u00f3n, Spain","institution_ids":["https://openalex.org/I165339363"]},{"raw_affiliation_string":"Department of Mathematics, University of Oviedo, Gijon, Spain#TAB#","institution_ids":["https://openalex.org/I165339363"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005658480","display_name":"J. M. Grau","orcid":"https://orcid.org/0000-0001-6652-0509"},"institutions":[{"id":"https://openalex.org/I165339363","display_name":"Universidad de Oviedo","ror":"https://ror.org/006gksa02","country_code":"ES","type":"education","lineage":["https://openalex.org/I165339363"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"J. M. Grau","raw_affiliation_strings":["Department of Mathematics , University of Oviedo , Campus of Viesques, Gij\u00f3n, Spain","Department of Mathematics, University of Oviedo, Gijon, Spain#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , University of Oviedo , Campus of Viesques, Gij\u00f3n, Spain","institution_ids":["https://openalex.org/I165339363"]},{"raw_affiliation_string":"Department of Mathematics, University of Oviedo, Gijon, Spain#TAB#","institution_ids":["https://openalex.org/I165339363"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102980879","display_name":"M. M. Ruiz","orcid":"https://orcid.org/0000-0001-9366-1956"},"institutions":[{"id":"https://openalex.org/I165339363","display_name":"Universidad de Oviedo","ror":"https://ror.org/006gksa02","country_code":"ES","type":"education","lineage":["https://openalex.org/I165339363"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"M. M. Ruiz","raw_affiliation_strings":["Department of Mathematics , University of Oviedo , Campus of Viesques, Gij\u00f3n, Spain","Department of Mathematics, University of Oviedo, Gijon, Spain#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , University of Oviedo , Campus of Viesques, Gij\u00f3n, Spain","institution_ids":["https://openalex.org/I165339363"]},{"raw_affiliation_string":"Department of Mathematics, University of Oviedo, Gijon, Spain#TAB#","institution_ids":["https://openalex.org/I165339363"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072145355","display_name":"P. M. Su\u00e1rez","orcid":"https://orcid.org/0000-0001-8968-8849"},"institutions":[{"id":"https://openalex.org/I165339363","display_name":"Universidad de Oviedo","ror":"https://ror.org/006gksa02","country_code":"ES","type":"education","lineage":["https://openalex.org/I165339363"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"P. M. Su\u00e1rez","raw_affiliation_strings":["Department of Mathematics , University of Oviedo , Campus of Viesques, Gij\u00f3n, Spain","Department of Mathematics, University of Oviedo, Gijon, Spain#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , University of Oviedo , Campus of Viesques, Gij\u00f3n, Spain","institution_ids":["https://openalex.org/I165339363"]},{"raw_affiliation_string":"Department of Mathematics, University of Oviedo, Gijon, Spain#TAB#","institution_ids":["https://openalex.org/I165339363"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5046537826"],"corresponding_institution_ids":["https://openalex.org/I165339363"],"apc_list":null,"apc_paid":null,"fwci":1.0076,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.78984328,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"86","issue":"2","first_page":"237","last_page":"249"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10424","display_name":"Electric Power System Optimization","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/T10424","display_name":"Electric Power System Optimization","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/T11185","display_name":"Integrated Energy Systems Optimization","score":0.9825000166893005,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/T10603","display_name":"Smart Grid Energy Management","score":0.9810000061988831,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/mathematical-optimization","display_name":"Mathematical optimization","score":0.6804600954055786},{"id":"https://openalex.org/keywords/electricity-market","display_name":"Electricity market","score":0.6456797122955322},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5992519855499268},{"id":"https://openalex.org/keywords/maximum-principle","display_name":"Maximum principle","score":0.5813379287719727},{"id":"https://openalex.org/keywords/electricity","display_name":"Electricity","score":0.5301761627197266},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.5259509086608887},{"id":"https://openalex.org/keywords/augmented-lagrangian-method","display_name":"Augmented Lagrangian method","score":0.49374422430992126},{"id":"https://openalex.org/keywords/variational-inequality","display_name":"Variational inequality","score":0.49367961287498474},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.4559422731399536},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.40933793783187866}],"concepts":[{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6804600954055786},{"id":"https://openalex.org/C146733006","wikidata":"https://www.wikidata.org/wiki/Q676081","display_name":"Electricity market","level":3,"score":0.6456797122955322},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5992519855499268},{"id":"https://openalex.org/C31010330","wikidata":"https://www.wikidata.org/wiki/Q1914255","display_name":"Maximum principle","level":3,"score":0.5813379287719727},{"id":"https://openalex.org/C206658404","wikidata":"https://www.wikidata.org/wiki/Q12725","display_name":"Electricity","level":2,"score":0.5301761627197266},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.5259509086608887},{"id":"https://openalex.org/C150452318","wikidata":"https://www.wikidata.org/wiki/Q4820432","display_name":"Augmented Lagrangian method","level":2,"score":0.49374422430992126},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.49367961287498474},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.4559422731399536},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.40933793783187866},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1080/00207160701864483","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160701864483","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"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":"International Journal of Computer Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.670.3751","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.670.3751","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.unioviedo.es/bayon/osh/abscmmse2007.pdf","raw_type":"text"},{"id":"pmh:oai:digibuo.uniovi.es:10651/8445","is_oa":true,"landing_page_url":"http://hdl.handle.net/10651/8445","pdf_url":null,"source":{"id":"https://openalex.org/S4306402334","display_name":"Consultation of the Doctoral Thesis Database (TESEO) (Ministerio de Educaci\u00f3n, Cultura y Deporte)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801976130","host_organization_name":"Ministerio de Educaci\u00f3n Cultura y Deporte","host_organization_lineage":["https://openalex.org/I2801976130"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SCOPUS","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:digibuo.uniovi.es:10651/8445","is_oa":true,"landing_page_url":"http://hdl.handle.net/10651/8445","pdf_url":null,"source":{"id":"https://openalex.org/S4306402334","display_name":"Consultation of the Doctoral Thesis Database (TESEO) (Ministerio de Educaci\u00f3n, Cultura y Deporte)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801976130","host_organization_name":"Ministerio de Educaci\u00f3n Cultura y Deporte","host_organization_lineage":["https://openalex.org/I2801976130"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SCOPUS","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W113562381","https://openalex.org/W1506895795","https://openalex.org/W1551360398","https://openalex.org/W1571403844","https://openalex.org/W1971947347","https://openalex.org/W1982650427","https://openalex.org/W1990306921","https://openalex.org/W1995533751","https://openalex.org/W2053120731","https://openalex.org/W2067893204","https://openalex.org/W2071741861","https://openalex.org/W2097671034","https://openalex.org/W2120406656","https://openalex.org/W2128471850","https://openalex.org/W2139303242","https://openalex.org/W2148772475","https://openalex.org/W2153136237","https://openalex.org/W2153355381","https://openalex.org/W2158547185","https://openalex.org/W2163676432","https://openalex.org/W2798574506","https://openalex.org/W4253133451","https://openalex.org/W4299637698","https://openalex.org/W6750621182"],"related_works":["https://openalex.org/W2962746246","https://openalex.org/W1967384683","https://openalex.org/W4292923857","https://openalex.org/W4302321938","https://openalex.org/W162218241","https://openalex.org/W2618936491","https://openalex.org/W4285534277","https://openalex.org/W1989531755","https://openalex.org/W1995052494","https://openalex.org/W3209004265"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"the":[3,30,35,57,73,78,84,90,107,114,117],"new":[4],"short-term":[5],"problems":[6],"that":[7],"are":[8,19,123],"faced":[9],"by":[10,100],"a":[11,15,46,69,120],"generation":[12],"company":[13],"in":[14,106],"deregulated":[16],"electricity":[17,38],"market":[18,32],"addressed":[20],"and":[21,63,89],"an":[22,40,103],"optimization":[23,52],"algorithm":[24,104],"is":[25,98],"proposed.":[26],"Our":[27],"model":[28],"of":[29,37,50,80,102,113,116],"spot":[31],"explicitly":[33],"represents":[34],"price":[36],"as":[39],"uncertain":[41],"exogenous":[42],"variable.":[43],"We":[44],"consider":[45],"very":[47],"complex":[48],"problem":[49,58,74,97],"hydrothermal":[51],"with":[53,60],"pumped-storage":[54],"plants,":[55],"so":[56],"deals":[59],"non-regular":[61],"Lagrangian":[62],"non-holonomic":[64],"inequality":[65],"constraints.":[66],"To":[67],"obtain":[68],"necessary":[70],"minimum":[71],"condition,":[72],"was":[75],"formulated":[76],"within":[77],"framework":[79],"nonsmooth":[81],"analysis":[82],"using":[83],"generalized":[85],"(or":[86],"Clarke's)":[87],"gradient":[88],"Nonsmooth":[91],"maximum":[92],"principle.":[93],"The":[94],"optimal":[95],"control":[96],"solved":[99],"means":[101],"implemented":[105],"commercial":[108],"software":[109],"package":[110],"Mathematica.":[111],"Results":[112],"application":[115],"method":[118],"to":[119],"numerical":[121],"example":[122],"presented.":[124]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
