{"id":"https://openalex.org/W2278603371","doi":"https://doi.org/10.1007/s10851-016-0663-7","title":"Techniques for Gradient-Based Bilevel Optimization with Non-smooth Lower Level Problems","display_name":"Techniques for Gradient-Based Bilevel Optimization with Non-smooth Lower Level Problems","publication_year":2016,"publication_date":"2016-05-17","ids":{"openalex":"https://openalex.org/W2278603371","doi":"https://doi.org/10.1007/s10851-016-0663-7","mag":"2278603371"},"language":"en","primary_location":{"id":"doi:10.1007/s10851-016-0663-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10851-016-0663-7","pdf_url":null,"source":{"id":"https://openalex.org/S66221708","display_name":"Journal of Mathematical Imaging and Vision","issn_l":"0924-9907","issn":["0924-9907","1573-7683"],"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":"Journal of Mathematical Imaging and Vision","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/A5082194697","display_name":"Peter Ochs","orcid":"https://orcid.org/0000-0002-4880-7511"},"institutions":[{"id":"https://openalex.org/I161046081","display_name":"University of Freiburg","ror":"https://ror.org/0245cg223","country_code":"DE","type":"education","lineage":["https://openalex.org/I161046081"]},{"id":"https://openalex.org/I91712215","display_name":"Saarland University","ror":"https://ror.org/01jdpyv68","country_code":"DE","type":"education","lineage":["https://openalex.org/I91712215"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Peter Ochs","raw_affiliation_strings":["Computer Vision Group, University of Freiburg, Freiburg im Breisgau, Germany","Mathematical Image Analysis Group, University of Saarland, Saarbr\u00fccken, Germany"],"affiliations":[{"raw_affiliation_string":"Computer Vision Group, University of Freiburg, Freiburg im Breisgau, Germany","institution_ids":["https://openalex.org/I161046081"]},{"raw_affiliation_string":"Mathematical Image Analysis Group, University of Saarland, Saarbr\u00fccken, Germany","institution_ids":["https://openalex.org/I91712215"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076203786","display_name":"Ren\u00e9 Ranftl","orcid":"https://orcid.org/0000-0003-4158-2759"},"institutions":[{"id":"https://openalex.org/I1343180700","display_name":"Intel (United States)","ror":"https://ror.org/01ek73717","country_code":"US","type":"company","lineage":["https://openalex.org/I1343180700"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ren\u00e9 Ranftl","raw_affiliation_strings":["Visual Computing Lab, Intel Labs, Santa Clara, CA, USA"],"affiliations":[{"raw_affiliation_string":"Visual Computing Lab, Intel Labs, Santa Clara, CA, USA","institution_ids":["https://openalex.org/I1343180700"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070290355","display_name":"Thomas Brox","orcid":"https://orcid.org/0000-0002-6282-8861"},"institutions":[{"id":"https://openalex.org/I161046081","display_name":"University of Freiburg","ror":"https://ror.org/0245cg223","country_code":"DE","type":"education","lineage":["https://openalex.org/I161046081"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Thomas Brox","raw_affiliation_strings":["Computer Vision Group, University of Freiburg, Freiburg im Breisgau, Germany"],"affiliations":[{"raw_affiliation_string":"Computer Vision Group, University of Freiburg, Freiburg im Breisgau, Germany","institution_ids":["https://openalex.org/I161046081"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5032205387","display_name":"Thomas Pock","orcid":"https://orcid.org/0000-0001-6120-1058"},"institutions":[{"id":"https://openalex.org/I4092182","display_name":"Graz University of Technology","ror":"https://ror.org/00d7xrm67","country_code":"AT","type":"education","lineage":["https://openalex.org/I4092182"]},{"id":"https://openalex.org/I132118926","display_name":"Austrian Institute of Technology","ror":"https://ror.org/04knbh022","country_code":"AT","type":"facility","lineage":["https://openalex.org/I132118926"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Thomas Pock","raw_affiliation_strings":["Digital Safety & Security Department, AIT Austrian Institute of Technology GmbH, 1220, Vienna, Austria","Institute for Computer Graphics and Vision, Graz University of Technology, Graz, Austria"],"affiliations":[{"raw_affiliation_string":"Digital Safety & Security Department, AIT Austrian Institute of Technology GmbH, 1220, Vienna, Austria","institution_ids":["https://openalex.org/I132118926"]},{"raw_affiliation_string":"Institute for Computer Graphics and Vision, Graz University of Technology, Graz, Austria","institution_ids":["https://openalex.org/I4092182"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5082194697"],"corresponding_institution_ids":["https://openalex.org/I161046081","https://openalex.org/I91712215"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2780},"apc_paid":null,"fwci":5.0314,"has_fulltext":false,"cited_by_count":47,"citation_normalized_percentile":{"value":0.95257786,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"56","issue":"2","first_page":"175","last_page":"194"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9991999864578247,"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":0.9991999864578247,"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":0.9943000078201294,"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/T11413","display_name":"Risk and Portfolio Optimization","score":0.9839000105857849,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/bilevel-optimization","display_name":"Bilevel optimization","score":0.7644283771514893},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.7152532935142517},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.7119519710540771},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.672144889831543},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6320608258247375},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.4971051514148712},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.48890891671180725},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3441067337989807},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3303864002227783}],"concepts":[{"id":"https://openalex.org/C3309286","wikidata":"https://www.wikidata.org/wiki/Q4907693","display_name":"Bilevel optimization","level":3,"score":0.7644283771514893},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.7152532935142517},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.7119519710540771},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.672144889831543},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6320608258247375},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.4971051514148712},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.48890891671180725},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3441067337989807},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3303864002227783},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10851-016-0663-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10851-016-0663-7","pdf_url":null,"source":{"id":"https://openalex.org/S66221708","display_name":"Journal of Mathematical Imaging and Vision","issn_l":"0924-9907","issn":["0924-9907","1573-7683"],"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":"Journal of Mathematical Imaging and Vision","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1247369571","display_name":null,"funder_award_id":"BR 3815/8-1","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G3823577063","display_name":null,"funder_award_id":"No. Y729","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G3890393441","display_name":null,"funder_award_id":"No. I1148","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W33665412","https://openalex.org/W1593038947","https://openalex.org/W1840913791","https://openalex.org/W1868831826","https://openalex.org/W1878638972","https://openalex.org/W1903029394","https://openalex.org/W1963882359","https://openalex.org/W1967138577","https://openalex.org/W1970163214","https://openalex.org/W1998576973","https://openalex.org/W1999198760","https://openalex.org/W2000462146","https://openalex.org/W2012231377","https://openalex.org/W2013918710","https://openalex.org/W2016384870","https://openalex.org/W2019569173","https://openalex.org/W2033468335","https://openalex.org/W2049893860","https://openalex.org/W2051434435","https://openalex.org/W2052387674","https://openalex.org/W2078725149","https://openalex.org/W2092663520","https://openalex.org/W2105842272","https://openalex.org/W2124592697","https://openalex.org/W2129116030","https://openalex.org/W2146545011","https://openalex.org/W2156417353","https://openalex.org/W2158894942","https://openalex.org/W2171650716","https://openalex.org/W2187061624","https://openalex.org/W2198630576","https://openalex.org/W2241435520","https://openalex.org/W2254218369","https://openalex.org/W2257784670","https://openalex.org/W2287409372","https://openalex.org/W2327387119","https://openalex.org/W2416516526","https://openalex.org/W2478429860","https://openalex.org/W2499145065","https://openalex.org/W2536208356","https://openalex.org/W2618333386","https://openalex.org/W2964121744","https://openalex.org/W4249667877","https://openalex.org/W6636216704"],"related_works":["https://openalex.org/W2890257643","https://openalex.org/W1495503294","https://openalex.org/W2161149697","https://openalex.org/W255338418","https://openalex.org/W2340378315","https://openalex.org/W2013038594","https://openalex.org/W1604175135","https://openalex.org/W3090200643","https://openalex.org/W2602322400","https://openalex.org/W2795565301"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":11},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":5}],"updated_date":"2026-04-24T08:23:43.765630","created_date":"2025-10-10T00:00:00"}