{"id":"https://openalex.org/W2885878954","doi":"https://doi.org/10.1137/17m1156678","title":"Adaptive FISTA for Nonconvex Optimization","display_name":"Adaptive FISTA for Nonconvex Optimization","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2885878954","doi":"https://doi.org/10.1137/17m1156678","mag":"2885878954"},"language":"en","primary_location":{"id":"doi:10.1137/17m1156678","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1156678","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"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 Optimization","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1711.04343","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5082194697","display_name":"Peter Ochs","orcid":"https://orcid.org/0000-0002-4880-7511"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Peter Ochs","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5032205387","display_name":"Thomas Pock","orcid":"https://orcid.org/0000-0001-6120-1058"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Thomas Pock","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5082194697"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00570177,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"29","issue":"4","first_page":"2482","last_page":"2503"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9976000189781189,"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"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9976000189781189,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9922999739646912,"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/T12015","display_name":"Photoacoustic and Ultrasonic Imaging","score":0.9916999936103821,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical 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/proximal-gradient-methods","display_name":"Proximal Gradient Methods","score":0.7277005910873413},{"id":"https://openalex.org/keywords/extrapolation","display_name":"Extrapolation","score":0.6605280637741089},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6102409362792969},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5959110260009766},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5551757216453552},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5473939180374146},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.5418009161949158},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5078702569007874},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4841461777687073},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.48069483041763306},{"id":"https://openalex.org/keywords/line-search","display_name":"Line search","score":0.47545287013053894},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.4478680193424225},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.43322449922561646},{"id":"https://openalex.org/keywords/identity","display_name":"Identity (music)","score":0.41797709465026855},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.35131174325942993},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.32204607129096985},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.21227207779884338},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14469727873802185},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07786580920219421},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06930598616600037},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.05986672639846802},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.057022660970687866}],"concepts":[{"id":"https://openalex.org/C10494615","wikidata":"https://www.wikidata.org/wiki/Q17086765","display_name":"Proximal Gradient Methods","level":4,"score":0.7277005910873413},{"id":"https://openalex.org/C132459708","wikidata":"https://www.wikidata.org/wiki/Q744069","display_name":"Extrapolation","level":2,"score":0.6605280637741089},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6102409362792969},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5959110260009766},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5551757216453552},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5473939180374146},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.5418009161949158},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5078702569007874},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4841461777687073},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.48069483041763306},{"id":"https://openalex.org/C85522705","wikidata":"https://www.wikidata.org/wiki/Q3278015","display_name":"Line search","level":3,"score":0.47545287013053894},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.4478680193424225},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.43322449922561646},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.41797709465026855},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.35131174325942993},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32204607129096985},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.21227207779884338},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14469727873802185},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07786580920219421},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06930598616600037},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.05986672639846802},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.057022660970687866},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/17m1156678","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1156678","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"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 Optimization","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1711.04343","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1711.04343","pdf_url":"https://arxiv.org/pdf/1711.04343","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"mag:2885878954","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1711.04343.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1711.04343","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1711.04343","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1711.04343","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1711.04343","pdf_url":"https://arxiv.org/pdf/1711.04343","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1343565032","display_name":null,"funder_award_id":"OC 150/1-1","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G500307253","display_name":null,"funder_award_id":"640156","funder_id":"https://openalex.org/F4320334678","funder_display_name":"European Research Council"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320334678","display_name":"European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2885878954.pdf","grobid_xml":"https://content.openalex.org/works/W2885878954.grobid-xml"},"referenced_works_count":34,"referenced_works":["https://openalex.org/W1837565340","https://openalex.org/W1977600144","https://openalex.org/W1977905043","https://openalex.org/W1978926712","https://openalex.org/W1987083649","https://openalex.org/W1988720110","https://openalex.org/W1998045815","https://openalex.org/W2000359198","https://openalex.org/W2000462146","https://openalex.org/W2004160833","https://openalex.org/W2006262045","https://openalex.org/W2016278923","https://openalex.org/W2019569173","https://openalex.org/W2021721734","https://openalex.org/W2026393324","https://openalex.org/W2047003499","https://openalex.org/W2051434435","https://openalex.org/W2062320580","https://openalex.org/W2080844831","https://openalex.org/W2092663520","https://openalex.org/W2101868363","https://openalex.org/W2139146655","https://openalex.org/W2142224912","https://openalex.org/W2142274086","https://openalex.org/W2149414429","https://openalex.org/W2151568819","https://openalex.org/W2161761402","https://openalex.org/W2171413647","https://openalex.org/W2198227614","https://openalex.org/W2259139337","https://openalex.org/W2316564661","https://openalex.org/W2474669789","https://openalex.org/W2951948474","https://openalex.org/W2962706047"],"related_works":["https://openalex.org/W2767126220","https://openalex.org/W2027836534","https://openalex.org/W2947118266","https://openalex.org/W1490376812","https://openalex.org/W2913758774","https://openalex.org/W2969687526","https://openalex.org/W3099152187","https://openalex.org/W2891483646","https://openalex.org/W2238261533","https://openalex.org/W2747668064","https://openalex.org/W2049331426","https://openalex.org/W3200844982","https://openalex.org/W3121751383","https://openalex.org/W2521415408","https://openalex.org/W2997044101","https://openalex.org/W3197743078","https://openalex.org/W2746934669","https://openalex.org/W2945057709","https://openalex.org/W2962765074","https://openalex.org/W2765758579"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3,25,77],"propose":[4],"an":[5,34],"adaptively":[6],"extrapolated":[7],"proximal":[8,17,61,84],"gradient":[9,18],"method,":[10],"which":[11],"is":[12,50,65,93],"based":[13],"on":[14,98],"the":[15,28,47,90],"accelerated":[16],"method":[19,92],"(also":[20],"known":[21],"as":[22,74],"FISTA);":[23],"however,":[24],"locally":[26],"optimize":[27],"extrapolation":[29],"parameter":[30],"by":[31],"carrying":[32],"out":[33,42],"exact":[35],"(or":[36],"inexact)":[37],"line":[38],"search.":[39],"It":[40],"turns":[41],"that":[43],"in":[44,67,95],"some":[45],"situations,":[46],"proposed":[48],"algorithm":[49],"equivalent":[51],"to":[52],"a":[53,68,75,99],"class":[54],"of":[55,89],"SR1":[56],"(identity":[57],"minus":[58],"rank":[59],"1)":[60],"quasi-Newton":[62,85],"methods.":[63,86],"Convergence":[64],"proved":[66],"general":[69],"nonconvex":[70],"setting,":[71],"and":[72],"hence,":[73],"byproduct,":[76],"also":[78],"obtain":[79],"new":[80,91],"convergence":[81],"guarantees":[82],"for":[83],"The":[87],"efficiency":[88],"shown":[94],"numerical":[96],"experiments":[97],"sparsity":[100],"regularized":[101],"nonlinear":[102],"inverse":[103],"problem.":[104]},"counts_by_year":[],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}