{"id":"https://openalex.org/W2000462146","doi":"https://doi.org/10.1137/130942954","title":"iPiano: Inertial Proximal Algorithm for Nonconvex Optimization","display_name":"iPiano: Inertial Proximal Algorithm for Nonconvex Optimization","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2000462146","doi":"https://doi.org/10.1137/130942954","mag":"2000462146"},"language":"en","primary_location":{"id":"doi:10.1137/130942954","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130942954","pdf_url":null,"source":{"id":"https://openalex.org/S152600803","display_name":"SIAM Journal on Imaging Sciences","issn_l":"1936-4954","issn":["1936-4954"],"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 Imaging Sciences","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"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Peter Ochs","raw_affiliation_strings":["Albert-Ludwigs-University of Freiburg"],"affiliations":[{"raw_affiliation_string":"Albert-Ludwigs-University of Freiburg","institution_ids":["https://openalex.org/I161046081"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077938164","display_name":"Yunjin Chen","orcid":"https://orcid.org/0000-0002-4428-2797"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yunjin Chen","raw_affiliation_strings":["Institut f\u00fcr Maschinelles Sehen und Darstellen (7100)"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Maschinelles Sehen und Darstellen (7100)","institution_ids":[]}]},{"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/I4092182","display_name":"Graz University of Technology","ror":"https://ror.org/00d7xrm67","country_code":"AT","type":"education","lineage":["https://openalex.org/I4092182"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Thomas Brox","raw_affiliation_strings":[", Graz University of Technology#TAB#"],"affiliations":[{"raw_affiliation_string":", Graz University of Technology#TAB#","institution_ids":["https://openalex.org/I4092182"]}]},{"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":["Institut f\u00fcr Maschinelles Sehen und Darstellen (7100)"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Maschinelles Sehen und Darstellen (7100)","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5082194697"],"corresponding_institution_ids":["https://openalex.org/I161046081"],"apc_list":null,"apc_paid":null,"fwci":39.5885,"has_fulltext":false,"cited_by_count":452,"citation_normalized_percentile":{"value":0.99949497,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"7","issue":"2","first_page":"1388","last_page":"1419"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9962999820709229,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9925000071525574,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5760464072227478},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5452133417129517},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5427132248878479},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.5164316296577454},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.49017244577407837},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.4549843370914459},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4502161145210266},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.44648388028144836},{"id":"https://openalex.org/keywords/ball","display_name":"Ball (mathematics)","score":0.43227988481521606},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.42294520139694214},{"id":"https://openalex.org/keywords/variational-inequality","display_name":"Variational inequality","score":0.4130741059780121},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3777504563331604},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3543204963207245},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.3495069444179535},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1179366409778595},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08578541874885559}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5760464072227478},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5452133417129517},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5427132248878479},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.5164316296577454},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.49017244577407837},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.4549843370914459},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4502161145210266},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.44648388028144836},{"id":"https://openalex.org/C122041747","wikidata":"https://www.wikidata.org/wiki/Q838611","display_name":"Ball (mathematics)","level":2,"score":0.43227988481521606},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.42294520139694214},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.4130741059780121},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3777504563331604},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3543204963207245},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.3495069444179535},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1179366409778595},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08578541874885559},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","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},{"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/130942954","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130942954","pdf_url":null,"source":{"id":"https://openalex.org/S152600803","display_name":"SIAM Journal on Imaging Sciences","issn_l":"1936-4954","issn":["1936-4954"],"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 Imaging Sciences","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.5099999904632568}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W19725371","https://openalex.org/W199410564","https://openalex.org/W205960364","https://openalex.org/W1524647815","https://openalex.org/W1586517188","https://openalex.org/W1720236078","https://openalex.org/W1840913791","https://openalex.org/W1946620893","https://openalex.org/W1967138577","https://openalex.org/W1969387119","https://openalex.org/W1979896658","https://openalex.org/W1988720110","https://openalex.org/W1989464734","https://openalex.org/W2006262045","https://openalex.org/W2013243898","https://openalex.org/W2013918710","https://openalex.org/W2019569173","https://openalex.org/W2020999234","https://openalex.org/W2021548137","https://openalex.org/W2022541060","https://openalex.org/W2030161963","https://openalex.org/W2038497950","https://openalex.org/W2040006905","https://openalex.org/W2048742402","https://openalex.org/W2051434435","https://openalex.org/W2058532290","https://openalex.org/W2062184313","https://openalex.org/W2068357778","https://openalex.org/W2078853581","https://openalex.org/W2088616581","https://openalex.org/W2092663520","https://openalex.org/W2100556411","https://openalex.org/W2126621530","https://openalex.org/W2129732816","https://openalex.org/W2130184048","https://openalex.org/W2139643804","https://openalex.org/W2152132615","https://openalex.org/W2158449358","https://openalex.org/W2162361955","https://openalex.org/W2171413647","https://openalex.org/W2331639718","https://openalex.org/W2798766386","https://openalex.org/W3141595720","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W4285277090","https://openalex.org/W4327738859","https://openalex.org/W2348722996","https://openalex.org/W2334570605","https://openalex.org/W4385382439","https://openalex.org/W4292651679","https://openalex.org/W2400034325","https://openalex.org/W2499557797","https://openalex.org/W2985014567","https://openalex.org/W4299515259"],"abstract_inverted_index":{"In":[0],"this":[1,129],"paper":[2],"we":[3],"study":[4],"an":[5,31,109],"algorithm":[6,25,54,74,116],"for":[7,55,76,103,113,137],"solving":[8],"a":[9,14,19,39,93,114,132],"minimization":[10],"problem":[11,140],"composed":[12],"of":[13,43,52,59,64,128],"differentiable":[15],"(possibly":[16,21],"nonconvex)":[17],"and":[18,68,119,153],"convex":[20],"nondifferentiable)":[22],"function.":[23],"The":[24,81],"iPiano":[26,121,144],"combines":[27],"forward-backward":[28],"splitting":[29],"with":[30,150],"inertial":[32],"force.":[33],"It":[34],"can":[35],"be":[36],"seen":[37],"as":[38],"nonsmooth":[40],"split":[41],"version":[42],"the":[44,53,56,65,69,73,88,126,138],"Heavy-ball":[45],"method":[46],"from":[47],"Polyak.":[48],"A":[49],"rigorous":[50],"analysis":[51],"proposed":[57],"class":[58],"problems":[60],"yields":[61],"global":[62],"convergence":[63,82,102,111,133],"function":[66],"values":[67],"arguments.":[70],"This":[71,91],"makes":[72],"robust":[75],"usage":[77],"on":[78,87,145],"nonconvex":[79],"problems.":[80],"result":[83],"is":[84,92,117,122,135],"obtained":[85],"based":[86,155],"Kurdyka--\u0141ojasiewicz":[89],"inequality.":[90],"very":[94],"weak":[95],"restriction,":[96],"which":[97],"was":[98],"used":[99],"to":[100,124],"prove":[101],"several":[104],"other":[105],"gradient":[106],"methods.":[107],"First,":[108],"abstract":[110],"theorem":[112],"generic":[115],"proved,":[118],"then":[120],"shown":[123],"satisfy":[125],"requirements":[127],"theorem.":[130],"Furthermore,":[131],"rate":[134],"established":[136],"general":[139],"class.":[141],"We":[142],"demonstrate":[143],"computer":[146],"vision":[147],"problems---image":[148],"denoising":[149],"learned":[151],"priors":[152],"diffusion":[154],"image":[156],"compression.":[157]},"counts_by_year":[{"year":2026,"cited_by_count":9},{"year":2025,"cited_by_count":37},{"year":2024,"cited_by_count":29},{"year":2023,"cited_by_count":46},{"year":2022,"cited_by_count":37},{"year":2021,"cited_by_count":52},{"year":2020,"cited_by_count":37},{"year":2019,"cited_by_count":42},{"year":2018,"cited_by_count":40},{"year":2017,"cited_by_count":38},{"year":2016,"cited_by_count":42},{"year":2015,"cited_by_count":33},{"year":2014,"cited_by_count":10}],"updated_date":"2026-04-14T08:04:32.555800","created_date":"2025-10-10T00:00:00"}
