{"id":"https://openalex.org/W4407181882","doi":"https://doi.org/10.1007/s10107-025-02194-4","title":"On penalty-based bilevel gradient descent method","display_name":"On penalty-based bilevel gradient descent method","publication_year":2025,"publication_date":"2025-02-05","ids":{"openalex":"https://openalex.org/W4407181882","doi":"https://doi.org/10.1007/s10107-025-02194-4"},"language":"en","primary_location":{"id":"doi:10.1007/s10107-025-02194-4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10107-025-02194-4","pdf_url":null,"source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming","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/A5001223413","display_name":"Han Shen","orcid":"https://orcid.org/0000-0001-8537-9862"},"institutions":[{"id":"https://openalex.org/I165799507","display_name":"Rensselaer Polytechnic Institute","ror":"https://ror.org/01rtyzb94","country_code":"US","type":"education","lineage":["https://openalex.org/I165799507"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Han Shen","raw_affiliation_strings":["Department of Electrical, Computer, and Systems Engineering, Rensselaer Polytechnic Institute, Troy, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical, Computer, and Systems Engineering, Rensselaer Polytechnic Institute, Troy, USA","institution_ids":["https://openalex.org/I165799507"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101535527","display_name":"Quan Xiao","orcid":"https://orcid.org/0009-0008-8492-0037"},"institutions":[{"id":"https://openalex.org/I165799507","display_name":"Rensselaer Polytechnic Institute","ror":"https://ror.org/01rtyzb94","country_code":"US","type":"education","lineage":["https://openalex.org/I165799507"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Quan Xiao","raw_affiliation_strings":["Department of Electrical, Computer, and Systems Engineering, Rensselaer Polytechnic Institute, Troy, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical, Computer, and Systems Engineering, Rensselaer Polytechnic Institute, Troy, USA","institution_ids":["https://openalex.org/I165799507"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100783471","display_name":"Tianyi Chen","orcid":"https://orcid.org/0000-0002-5829-051X"},"institutions":[{"id":"https://openalex.org/I165799507","display_name":"Rensselaer Polytechnic Institute","ror":"https://ror.org/01rtyzb94","country_code":"US","type":"education","lineage":["https://openalex.org/I165799507"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Tianyi Chen","raw_affiliation_strings":["Department of Electrical, Computer, and Systems Engineering, Rensselaer Polytechnic Institute, Troy, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical, Computer, and Systems Engineering, Rensselaer Polytechnic Institute, Troy, USA","institution_ids":["https://openalex.org/I165799507"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100783471"],"corresponding_institution_ids":["https://openalex.org/I165799507"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":11.518,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.98379096,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":98},"biblio":{"volume":"214","issue":"1-2","first_page":"539","last_page":"589"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9934999942779541,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.991599977016449,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/penalty-method","display_name":"Penalty method","score":0.7475391030311584},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7155717015266418},{"id":"https://openalex.org/keywords/bilevel-optimization","display_name":"Bilevel optimization","score":0.5661888122558594},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5158911943435669},{"id":"https://openalex.org/keywords/gradient-method","display_name":"Gradient method","score":0.48030227422714233},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4672168493270874},{"id":"https://openalex.org/keywords/descent","display_name":"Descent (aeronautics)","score":0.45920947194099426},{"id":"https://openalex.org/keywords/variational-inequality","display_name":"Variational inequality","score":0.45742571353912354},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.4538671672344208},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4396522045135498},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.2399996519088745},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2188219428062439},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.16209304332733154},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.11224427819252014}],"concepts":[{"id":"https://openalex.org/C6180225","wikidata":"https://www.wikidata.org/wiki/Q3411771","display_name":"Penalty method","level":2,"score":0.7475391030311584},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7155717015266418},{"id":"https://openalex.org/C3309286","wikidata":"https://www.wikidata.org/wiki/Q4907693","display_name":"Bilevel optimization","level":3,"score":0.5661888122558594},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5158911943435669},{"id":"https://openalex.org/C115680565","wikidata":"https://www.wikidata.org/wiki/Q5977448","display_name":"Gradient method","level":2,"score":0.48030227422714233},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4672168493270874},{"id":"https://openalex.org/C2776637919","wikidata":"https://www.wikidata.org/wiki/Q624380","display_name":"Descent (aeronautics)","level":2,"score":0.45920947194099426},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.45742571353912354},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.4538671672344208},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4396522045135498},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.2399996519088745},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2188219428062439},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.16209304332733154},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.11224427819252014},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace 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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10107-025-02194-4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10107-025-02194-4","pdf_url":null,"source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Climate action","id":"https://metadata.un.org/sdg/13","score":0.47999998927116394}],"awards":[{"id":"https://openalex.org/G399095212","display_name":null,"funder_award_id":"2134168","funder_id":"https://openalex.org/F4320332172","funder_display_name":"Directorate for Mathematical and Physical Sciences"},{"id":"https://openalex.org/G637883758","display_name":null,"funder_award_id":"2047177","funder_id":"https://openalex.org/F4320337392","funder_display_name":"Division of Electrical, Communications and Cyber Systems"}],"funders":[{"id":"https://openalex.org/F4320307762","display_name":"International Business Machines Corporation","ror":"https://ror.org/05hh8d621"},{"id":"https://openalex.org/F4320307791","display_name":"Cisco Systems","ror":"https://ror.org/03yt1ez60"},{"id":"https://openalex.org/F4320332172","display_name":"Directorate for Mathematical and Physical Sciences","ror":"https://ror.org/029b7h395"},{"id":"https://openalex.org/F4320337392","display_name":"Division of Electrical, Communications and Cyber Systems","ror":"https://ror.org/01krpsy48"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W1494085563","https://openalex.org/W1551360398","https://openalex.org/W1968859249","https://openalex.org/W1983644172","https://openalex.org/W1990676004","https://openalex.org/W2005629858","https://openalex.org/W2009941369","https://openalex.org/W2029463628","https://openalex.org/W2030161963","https://openalex.org/W2044241503","https://openalex.org/W2048223470","https://openalex.org/W2054118322","https://openalex.org/W2077161157","https://openalex.org/W2100556411","https://openalex.org/W2124659975","https://openalex.org/W2126813526","https://openalex.org/W2128255043","https://openalex.org/W2606904667","https://openalex.org/W2963248893","https://openalex.org/W2963353224","https://openalex.org/W2963534244","https://openalex.org/W2979541819","https://openalex.org/W3087823096","https://openalex.org/W3123350987","https://openalex.org/W3158971458","https://openalex.org/W3199051821","https://openalex.org/W4200629126","https://openalex.org/W4205293988","https://openalex.org/W4224932938","https://openalex.org/W4226038297","https://openalex.org/W4231147659","https://openalex.org/W4231183558","https://openalex.org/W4296062046","https://openalex.org/W4317897806","https://openalex.org/W4318040964","https://openalex.org/W4393190086","https://openalex.org/W6600648412","https://openalex.org/W6601712973"],"related_works":["https://openalex.org/W1988507758","https://openalex.org/W3148242583","https://openalex.org/W1994921083","https://openalex.org/W2108630901","https://openalex.org/W2783384756","https://openalex.org/W1518141773","https://openalex.org/W2810700601","https://openalex.org/W2330339184","https://openalex.org/W2013038594","https://openalex.org/W1970816989"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3}],"updated_date":"2026-06-13T06:13:01.061226","created_date":"2025-10-10T00:00:00"}
