{"id":"https://openalex.org/W3033314443","doi":"https://doi.org/10.1007/s10898-021-01070-7","title":"On nondegenerate M-stationary points for sparsity constrained nonlinear optimization","display_name":"On nondegenerate M-stationary points for sparsity constrained nonlinear optimization","publication_year":2021,"publication_date":"2021-08-23","ids":{"openalex":"https://openalex.org/W3033314443","doi":"https://doi.org/10.1007/s10898-021-01070-7","mag":"3033314443"},"language":"en","primary_location":{"id":"doi:10.1007/s10898-021-01070-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10898-021-01070-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10898-021-01070-7.pdf","source":{"id":"https://openalex.org/S115925768","display_name":"Journal of Global Optimization","issn_l":"0925-5001","issn":["0925-5001","1573-2916"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Global Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10898-021-01070-7.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5071503953","display_name":"Sebastian L\u00e4mmel","orcid":"https://orcid.org/0000-0001-5064-7249"},"institutions":[{"id":"https://openalex.org/I2610724","display_name":"Chemnitz University of Technology","ror":"https://ror.org/00a208s56","country_code":"DE","type":"education","lineage":["https://openalex.org/I2610724"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"S. L\u00e4mmel","raw_affiliation_strings":["Department of Mathematics, Chemnitz University of Technology, Chemnitz, Germany","[Chemnitz University of Technology]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Chemnitz University of Technology, Chemnitz, Germany","institution_ids":["https://openalex.org/I2610724"]},{"raw_affiliation_string":"[Chemnitz University of Technology]","institution_ids":["https://openalex.org/I2610724"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035961103","display_name":"Vladimir Shikhman","orcid":"https://orcid.org/0000-0002-8031-6069"},"institutions":[{"id":"https://openalex.org/I2610724","display_name":"Chemnitz University of Technology","ror":"https://ror.org/00a208s56","country_code":"DE","type":"education","lineage":["https://openalex.org/I2610724"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"V. Shikhman","raw_affiliation_strings":["Department of Mathematics, Chemnitz University of Technology, Chemnitz, Germany","[Chemnitz University of Technology]"],"raw_orcid":"https://orcid.org/0000-0002-8031-6069","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Chemnitz University of Technology, Chemnitz, Germany","institution_ids":["https://openalex.org/I2610724"]},{"raw_affiliation_string":"[Chemnitz University of Technology]","institution_ids":["https://openalex.org/I2610724"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5035961103"],"corresponding_institution_ids":["https://openalex.org/I2610724"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":{"value":2990,"currency":"USD","value_usd":2990},"fwci":0.1536,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.3668579,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":93},"biblio":{"volume":"82","issue":"2","first_page":"219","last_page":"242"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9961000084877014,"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":0.9961000084877014,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9958000183105469,"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/T11308","display_name":"Sphingolipid Metabolism and Signaling","score":0.986299991607666,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/stationary-point","display_name":"Stationary point","score":0.8125631809234619},{"id":"https://openalex.org/keywords/saddle-point","display_name":"Saddle point","score":0.8121014833450317},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6182833313941956},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.48901256918907166},{"id":"https://openalex.org/keywords/degeneracy","display_name":"Degeneracy (biology)","score":0.4468937814235687},{"id":"https://openalex.org/keywords/morse-theory","display_name":"Morse theory","score":0.43782609701156616},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4215620756149292},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.41977548599243164},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.41311779618263245},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.39185765385627747},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3794136643409729},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.18021130561828613},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1230926513671875},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.0829818844795227}],"concepts":[{"id":"https://openalex.org/C189237950","wikidata":"https://www.wikidata.org/wiki/Q2500758","display_name":"Stationary point","level":2,"score":0.8125631809234619},{"id":"https://openalex.org/C2681867","wikidata":"https://www.wikidata.org/wiki/Q690935","display_name":"Saddle point","level":2,"score":0.8121014833450317},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6182833313941956},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.48901256918907166},{"id":"https://openalex.org/C2777727622","wikidata":"https://www.wikidata.org/wiki/Q5251772","display_name":"Degeneracy (biology)","level":2,"score":0.4468937814235687},{"id":"https://openalex.org/C156730297","wikidata":"https://www.wikidata.org/wiki/Q2296951","display_name":"Morse theory","level":2,"score":0.43782609701156616},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4215620756149292},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.41977548599243164},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.41311779618263245},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.39185765385627747},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3794136643409729},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.18021130561828613},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1230926513671875},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0829818844795227},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","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/C60644358","wikidata":"https://www.wikidata.org/wiki/Q128570","display_name":"Bioinformatics","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1007/s10898-021-01070-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10898-021-01070-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10898-021-01070-7.pdf","source":{"id":"https://openalex.org/S115925768","display_name":"Journal of Global Optimization","issn_l":"0925-5001","issn":["0925-5001","1573-2916"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Global Optimization","raw_type":"journal-article"},{"id":"mag:3033314443","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1912.04087.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":"pmh:oai:RePEc:spr:jglopt:v:82:y:2022:i:2:d:10.1007_s10898-021-01070-7","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10898-021-01070-7","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"},{"id":"pmh:oai:econstor.eu:10419/287145","is_oa":true,"landing_page_url":"https://hdl.handle.net/10419/287145","pdf_url":null,"source":{"id":"https://openalex.org/S4306401696","display_name":"Econstor (Econstor)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"doc-type:article"},{"id":"doi:10.48550/arxiv.1912.04087","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1912.04087","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":"doi:10.1007/s10898-021-01070-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10898-021-01070-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10898-021-01070-7.pdf","source":{"id":"https://openalex.org/S115925768","display_name":"Journal of Global Optimization","issn_l":"0925-5001","issn":["0925-5001","1573-2916"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Global Optimization","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320311034","display_name":"Technische Universit\u00e4t Chemnitz","ror":"https://ror.org/00a208s56"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3033314443.pdf","grobid_xml":"https://content.openalex.org/works/W3033314443.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W638016179","https://openalex.org/W1530632394","https://openalex.org/W1625584880","https://openalex.org/W1875533481","https://openalex.org/W1937543970","https://openalex.org/W2030661811","https://openalex.org/W2031197045","https://openalex.org/W2053249331","https://openalex.org/W2083346837","https://openalex.org/W2135046866","https://openalex.org/W2187547409","https://openalex.org/W2189653089","https://openalex.org/W2296616510","https://openalex.org/W2475678528","https://openalex.org/W2485484761","https://openalex.org/W2788039246","https://openalex.org/W2805222821","https://openalex.org/W2963579802","https://openalex.org/W3194851289","https://openalex.org/W3201876985","https://openalex.org/W4213143060","https://openalex.org/W4213199372","https://openalex.org/W4235840289","https://openalex.org/W4249513058","https://openalex.org/W4250955649","https://openalex.org/W4300596011"],"related_works":["https://openalex.org/W2068163052","https://openalex.org/W3201490813","https://openalex.org/W2517212518","https://openalex.org/W2156357125","https://openalex.org/W2963322394","https://openalex.org/W2977507153","https://openalex.org/W3010759471","https://openalex.org/W3013639021","https://openalex.org/W2161747494","https://openalex.org/W3200673791","https://openalex.org/W1994959064","https://openalex.org/W3161311214","https://openalex.org/W2771616066","https://openalex.org/W3157206654","https://openalex.org/W3098625010","https://openalex.org/W2953310296","https://openalex.org/W2010009791","https://openalex.org/W2138800629","https://openalex.org/W2949354093","https://openalex.org/W2950275456"],"abstract_inverted_index":{"Abstract":[0],"We":[1,48,57,245],"study":[2,138],"sparsity":[3,69],"constrained":[4],"nonlinear":[5],"optimization":[6,176],"(SCNO)":[7],"from":[8,21,220],"a":[9,78,186,190,233],"topological":[10,139],"point":[11,235],"of":[12,77,103,107,118,127,132,141,156,199,205,212,223,252,258],"view.":[13],"Special":[14],"focus":[15],"will":[16],"be":[17,165,217],"on":[18],"M-stationary":[19,51,61,148,203],"points":[20,36,52,62,108,204,215,254],"Burdakov":[22],"et":[23,39],"al.":[24,40],"(SIAM":[25],"J":[26],"Optim":[27],"26:397\u2013425,":[28],"2016),":[29],"also":[30],"introduced":[31],"as":[32,88],"$$N^C$$":[33],"NC":[34],"-stationary":[35],"in":[37,96,171,231],"Pan":[38],"(J":[41],"Oper":[42],"Res":[43],"Soc":[44],"China":[45],"3:421\u2013439,":[46],"2015).":[47],"introduce":[49],"nondegenerate":[50],"and":[53,92,105,202],"define":[54],"their":[55],"M-index.":[56],"show":[58],"that":[59,247],"all":[60,74],"are":[63,94,114,162],"generically":[64],"nondegenerate.":[65],"In":[66],"particular,":[67],"the":[68,101,124,130,160,197,221,228,248,256],"constraint":[70],"is":[71,170,255],"active":[72],"at":[73],"local":[75,200,243],"minimizers":[76,201],"generic":[79],"SCNO.":[80],"Some":[81],"relations":[82],"to":[83,110,121,159,164,208,227,238,264],"other":[84,175],"stationarity":[85,112],"concepts,":[86],"such":[87,213],"S-stationarity,":[89],"basic":[90],"feasibility,":[91],"CW-minimality,":[93],"discussed":[95],"detail.":[97],"By":[98],"doing":[99],"so,":[100],"issues":[102],"instability":[104],"degeneracy":[106],"due":[109],"different":[111,242],"concepts":[113],"highlighted.":[115],"The":[116,210],"concept":[117],"M-stationarity":[119],"allows":[120],"adequately":[122],"describe":[123],"global":[125,224,265],"structure":[126,251],"SCNO":[128,263],"along":[129],"lines":[131],"Morse":[133,191],"theory.":[134],"For":[135],"that,":[136],"we":[137,188],"changes":[140],"lower":[142],"level":[143],"sets":[144],"while":[145],"passing":[146],"an":[147],"point.":[149],"As":[150,185],"novelty":[151],"for":[152,193],"SCNO,":[153,194],"multiple":[154],"cells":[155],"dimension":[157],"equal":[158,207],"M-index":[161,206],"needed":[163],"attached.":[166],"This":[167],"intriguing":[168],"fact":[169],"strong":[172],"contrast":[173],"with":[174],"problems":[177],"considered":[178],"before,":[179],"where":[180],"just":[181],"one":[182],"cell":[183],"suffices.":[184],"consequence,":[187],"derive":[189],"relation":[192],"which":[195],"relates":[196],"numbers":[198],"one.":[209],"appearance":[211],"saddle":[214,234,253],"cannot":[216],"thus":[218],"neglected":[219],"perspective":[222],"optimization.":[225],"Due":[226],"multiplicity":[229],"phenomenon":[230],"cell-attachment,":[232],"may":[236],"lead":[237],"more":[239],"than":[240],"two":[241],"minimizers.":[244],"conclude":[246],"relatively":[249],"involved":[250],"source":[257],"well-known":[259],"difficulty":[260],"if":[261],"solving":[262],"optimality.":[266]},"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}