{"id":"https://openalex.org/W2792285932","doi":"https://doi.org/10.1137/18m1177019","title":"Large-Scale and Global Maximization of the Distance to Instability","display_name":"Large-Scale and Global Maximization of the Distance to Instability","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2792285932","doi":"https://doi.org/10.1137/18m1177019","mag":"2792285932"},"language":"en","primary_location":{"id":"doi:10.1137/18m1177019","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1177019","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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 Matrix Analysis and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1803.08712","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5024885694","display_name":"Emre Mengi","orcid":"https://orcid.org/0000-0003-0788-0066"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Emre Mengi","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0003-0788-0066","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5024885694"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.02702794,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"39","issue":"4","first_page":"1776","last_page":"1809"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9997000098228455,"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":0.9997000098228455,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9997000098228455,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.7585883140563965},{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.7401541471481323},{"id":"https://openalex.org/keywords/instability","display_name":"Instability","score":0.6785391569137573},{"id":"https://openalex.org/keywords/maximization","display_name":"Maximization","score":0.6310160160064697},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.6043717861175537},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6036342978477478},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5719150900840759},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5486350059509277},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.5104650259017944},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5065568685531616},{"id":"https://openalex.org/keywords/scale","display_name":"Scale (ratio)","score":0.47566741704940796},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.39007553458213806},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.38770371675491333},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15068009495735168},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10265141725540161},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.09182602167129517},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.07652464509010315},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.06692638993263245}],"concepts":[{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.7585883140563965},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.7401541471481323},{"id":"https://openalex.org/C207821765","wikidata":"https://www.wikidata.org/wiki/Q405372","display_name":"Instability","level":2,"score":0.6785391569137573},{"id":"https://openalex.org/C2776330181","wikidata":"https://www.wikidata.org/wiki/Q18358244","display_name":"Maximization","level":2,"score":0.6310160160064697},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.6043717861175537},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6036342978477478},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5719150900840759},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5486350059509277},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5104650259017944},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5065568685531616},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.47566741704940796},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.39007553458213806},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38770371675491333},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15068009495735168},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10265141725540161},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.09182602167129517},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.07652464509010315},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.06692638993263245},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/18m1177019","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1177019","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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 Matrix Analysis and Applications","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1803.08712","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1803.08712","pdf_url":"https://arxiv.org/pdf/1803.08712","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":null},{"id":"pmh:oai:arXiv.org:1803.08712","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1803.08712","pdf_url":"https://arxiv.org/pdf/1803.08712","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":null,"raw_type":"text"},{"id":"mag:2792285932","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1803.08712.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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.1803.08712","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1803.08712","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1803.08712","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1803.08712","pdf_url":"https://arxiv.org/pdf/1803.08712","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":null},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320319918","display_name":"York University","ror":"https://ror.org/05fq50484"},{"id":"https://openalex.org/F4320320915","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2792285932.pdf","grobid_xml":"https://content.openalex.org/works/W2792285932.grobid-xml"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W594391557","https://openalex.org/W1536758725","https://openalex.org/W1975277883","https://openalex.org/W1984560319","https://openalex.org/W2007405464","https://openalex.org/W2012604200","https://openalex.org/W2029383729","https://openalex.org/W2032733248","https://openalex.org/W2037064199","https://openalex.org/W2039606278","https://openalex.org/W2047917018","https://openalex.org/W2054155441","https://openalex.org/W2064942524","https://openalex.org/W2090832914","https://openalex.org/W2107543637","https://openalex.org/W2128857230","https://openalex.org/W2130417105","https://openalex.org/W2147228817","https://openalex.org/W2164349943","https://openalex.org/W2178909929","https://openalex.org/W2180470641","https://openalex.org/W2209184911","https://openalex.org/W2284696297","https://openalex.org/W2552140239","https://openalex.org/W2589370651","https://openalex.org/W2610857016","https://openalex.org/W2616614818","https://openalex.org/W2798909945","https://openalex.org/W2963601630","https://openalex.org/W3044539670","https://openalex.org/W4242975128"],"related_works":["https://openalex.org/W3137286346","https://openalex.org/W2593299318","https://openalex.org/W3130799020","https://openalex.org/W2981653234","https://openalex.org/W947105725","https://openalex.org/W3211659246","https://openalex.org/W2499557797","https://openalex.org/W2804339962","https://openalex.org/W3110931384","https://openalex.org/W2972354402","https://openalex.org/W3206616218","https://openalex.org/W2964083304","https://openalex.org/W2202258464","https://openalex.org/W3211565379","https://openalex.org/W3081204256","https://openalex.org/W2784019040","https://openalex.org/W835513632","https://openalex.org/W2896204105","https://openalex.org/W3211283867","https://openalex.org/W2469560512"],"abstract_inverted_index":{"The":[0,113],"larger":[1],"the":[2,10,14,21,27,41,44,66,76,89,95,107,110,116,128,139],"distance":[3,45],"to":[4,46,62,138],"instability":[5,47],"from":[6],"a":[7,49,55,71,85,102,123,132],"matrix":[8,50,77,111],"is,":[9],"more":[11],"robustly":[12],"stable":[13],"associated":[15],"autonomous":[16],"dynamical":[17],"system":[18],"is":[19,60,78,120],"in":[20],"presence":[22],"of":[23,43,48,79,109,115],"uncertainties":[24],"and":[25,82,131],"typically":[26],"less":[28],"severe":[29],"transient":[30],"behavior":[31],"its":[32],"solution":[33],"exhibits.":[34],"Motivated":[35],"by":[36],"these":[37],"issues,":[38],"we":[39,69,92],"consider":[40],"maximization":[42],"dependent":[51],"on":[52,84],"several":[53],"parameters,":[54],"nonconvex":[56],"optimization":[57],"problem":[58],"that":[59,105],"likely":[61],"be":[63],"nonsmooth.":[64],"In":[65,88],"first":[67],"part":[68,91],"propose":[70],"globally":[72],"convergent":[73],"algorithm":[74],"when":[75],"small":[80],"size":[81,108],"depends":[83],"few":[86],"parameters.":[87],"second":[90],"deal":[93],"with":[94,122,136],"problems":[96],"involving":[97],"large":[98],"matrices.":[99],"We":[100],"tailor":[101],"subspace":[103,118,140],"framework":[104,119],"reduces":[106],"drastically.":[112],"strength":[114],"tailored":[117],"proven":[121],"global":[124],"convergence":[125],"result":[126,135],"as":[127],"subspaces":[129],"grow":[130],"superlinear":[133],"rate-of-convergence":[134],"respect":[137],"dimension.":[141]},"counts_by_year":[],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2025-10-10T00:00:00"}
