{"id":"https://openalex.org/W2183055901","doi":"https://doi.org/10.1109/icmlc.2015.7340657","title":"Improved equilibrium point algorithm of linear bilevel programming","display_name":"Improved equilibrium point algorithm of linear bilevel programming","publication_year":2015,"publication_date":"2015-07-01","ids":{"openalex":"https://openalex.org/W2183055901","doi":"https://doi.org/10.1109/icmlc.2015.7340657","mag":"2183055901"},"language":"en","primary_location":{"id":"doi:10.1109/icmlc.2015.7340657","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icmlc.2015.7340657","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 International Conference on Machine Learning and Cybernetics (ICMLC)","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/A5047550532","display_name":"Fangyuan Li","orcid":"https://orcid.org/0000-0002-2815-3602"},"institutions":[{"id":"https://openalex.org/I153473198","display_name":"North China Electric Power University","ror":"https://ror.org/04qr5t414","country_code":"CN","type":"education","lineage":["https://openalex.org/I153473198"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Fang-Yuan Li","raw_affiliation_strings":["Department of Mathematics and Physics, North China Electric Power University Baoding, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Physics, North China Electric Power University Baoding, China","institution_ids":["https://openalex.org/I153473198"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100734888","display_name":"Guoli Zhang","orcid":"https://orcid.org/0000-0002-2219-1683"},"institutions":[{"id":"https://openalex.org/I153473198","display_name":"North China Electric Power University","ror":"https://ror.org/04qr5t414","country_code":"CN","type":"education","lineage":["https://openalex.org/I153473198"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guo-Li Zhang","raw_affiliation_strings":["Department of Mathematics and Physics, North China Electric Power University Baoding, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Physics, North China Electric Power University Baoding, China","institution_ids":["https://openalex.org/I153473198"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5047550532"],"corresponding_institution_ids":["https://openalex.org/I153473198"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.09661263,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"25","issue":null,"first_page":"809","last_page":"814"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9991000294685364,"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":0.9991000294685364,"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/T12546","display_name":"Smart Parking Systems Research","score":0.9934999942779541,"subfield":{"id":"https://openalex.org/subfields/2215","display_name":"Building and Construction"},"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/T10698","display_name":"Transportation Planning and Optimization","score":0.9847000241279602,"subfield":{"id":"https://openalex.org/subfields/3313","display_name":"Transportation"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6098228096961975},{"id":"https://openalex.org/keywords/bilevel-optimization","display_name":"Bilevel optimization","score":0.6083502769470215},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.6014175415039062},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6009376049041748},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.5522782206535339},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.5448926687240601},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5336086750030518},{"id":"https://openalex.org/keywords/criss-cross-algorithm","display_name":"Criss-cross algorithm","score":0.53285151720047},{"id":"https://openalex.org/keywords/interior-point-method","display_name":"Interior point method","score":0.4255017340183258},{"id":"https://openalex.org/keywords/bilinear-interpolation","display_name":"Bilinear interpolation","score":0.422640323638916},{"id":"https://openalex.org/keywords/equilibrium-point","display_name":"Equilibrium point","score":0.41263002157211304},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3569486737251282},{"id":"https://openalex.org/keywords/linear-fractional-programming","display_name":"Linear-fractional programming","score":0.3060065507888794},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.2042299509048462}],"concepts":[{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6098228096961975},{"id":"https://openalex.org/C3309286","wikidata":"https://www.wikidata.org/wiki/Q4907693","display_name":"Bilevel optimization","level":3,"score":0.6083502769470215},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.6014175415039062},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6009376049041748},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.5522782206535339},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.5448926687240601},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5336086750030518},{"id":"https://openalex.org/C52486349","wikidata":"https://www.wikidata.org/wiki/Q17006040","display_name":"Criss-cross algorithm","level":4,"score":0.53285151720047},{"id":"https://openalex.org/C155253501","wikidata":"https://www.wikidata.org/wiki/Q461992","display_name":"Interior point method","level":2,"score":0.4255017340183258},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.422640323638916},{"id":"https://openalex.org/C94766913","wikidata":"https://www.wikidata.org/wiki/Q1530271","display_name":"Equilibrium point","level":3,"score":0.41263002157211304},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3569486737251282},{"id":"https://openalex.org/C205658194","wikidata":"https://www.wikidata.org/wiki/Q4168281","display_name":"Linear-fractional programming","level":3,"score":0.3060065507888794},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.2042299509048462},{"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/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","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/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/icmlc.2015.7340657","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icmlc.2015.7340657","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 International Conference on Machine Learning and Cybernetics (ICMLC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W2018858795","https://openalex.org/W2032476260","https://openalex.org/W2069461775","https://openalex.org/W2095818975","https://openalex.org/W2112184561","https://openalex.org/W2355741217","https://openalex.org/W2357635757","https://openalex.org/W2361400422","https://openalex.org/W2369710229","https://openalex.org/W2373828676","https://openalex.org/W2377527717","https://openalex.org/W2481910659"],"related_works":["https://openalex.org/W4205348974","https://openalex.org/W4388279198","https://openalex.org/W1709621369","https://openalex.org/W61976518","https://openalex.org/W2367492128","https://openalex.org/W2114808974","https://openalex.org/W2006985686","https://openalex.org/W2030563458","https://openalex.org/W2318926272","https://openalex.org/W2136118765"],"abstract_inverted_index":{"In":[0],"this":[1,22],"paper,":[2],"an":[3,7],"algorithm":[4,23,44,79,97],"for":[5],"finding":[6],"\u03b5-globally":[8],"optimal":[9],"solution":[10],"of":[11,35],"the":[12,24,33,36,43,52,58,64,69,75,84,96],"linear":[13],"bilevel":[14],"programming":[15,60],"problem":[16],"(LBP)":[17],"is":[18,30,72,80,91],"considered.":[19],"We":[20,41],"call":[21],"improved":[25,76],"equilibrium":[26,38,66,77],"point":[27,39,67,78],"algorithm.":[28,40],"It":[29],"based":[31],"on":[32],"notion":[34],"basic":[37,65],"propose":[42],"by":[45],"adding":[46],"a":[47,88],"new":[48],"cutting":[49],"plan":[50],"in":[51,82],"constraint":[53],"conditions,":[54],"and":[55],"combining":[56],"with":[57,63],"bilinear":[59],"problem.":[61],"Compared":[62],"algorithm,":[68],"calculation":[70],"burden":[71],"reduced":[73],"when":[74],"used":[81],"solving":[83],"LBP.":[85],"At":[86],"last":[87],"numerical":[89],"example":[90],"given":[92],"to":[93],"illustrate":[94],"how":[95],"works.":[98]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}