{"id":"https://openalex.org/W2081194262","doi":"https://doi.org/10.1137/s0895479895290978","title":"Generalized Monotone Affine Maps","display_name":"Generalized Monotone Affine Maps","publication_year":1996,"publication_date":"1996-10-01","ids":{"openalex":"https://openalex.org/W2081194262","doi":"https://doi.org/10.1137/s0895479895290978","mag":"2081194262"},"language":"en","primary_location":{"id":"doi:10.1137/s0895479895290978","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479895290978","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":["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/A5022248421","display_name":"Jean-Pierre Crouzeix","orcid":"https://orcid.org/0000-0001-5874-457X"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Jean-Pierre Crouzeix","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5057911947","display_name":"Siegfried Schaible","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Siegfried Schaible","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5022248421"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.31454667,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.80534544,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"17","issue":"4","first_page":"992","last_page":"997"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9980999827384949,"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"}},"topics":[{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9980999827384949,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9977999925613403,"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/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9890000224113464,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.7950514554977417},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6949560642242432},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.6085406541824341},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.5502819418907166},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4824943542480469},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.47565194964408875},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.41634514927864075},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.38630619645118713},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.16587093472480774}],"concepts":[{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.7950514554977417},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6949560642242432},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.6085406541824341},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5502819418907166},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4824943542480469},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.47565194964408875},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.41634514927864075},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.38630619645118713},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.16587093472480774},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0895479895290978","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479895290978","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1965005753","https://openalex.org/W1968297122","https://openalex.org/W1969867455","https://openalex.org/W1990995401","https://openalex.org/W2020118917","https://openalex.org/W2032292661","https://openalex.org/W2036370633","https://openalex.org/W2047118504","https://openalex.org/W2055576996","https://openalex.org/W2065279254","https://openalex.org/W2085803700","https://openalex.org/W2092169411","https://openalex.org/W2094737495","https://openalex.org/W2144997132","https://openalex.org/W2274153042","https://openalex.org/W4248623816"],"related_works":["https://openalex.org/W1996444892","https://openalex.org/W1976810887","https://openalex.org/W1985218657","https://openalex.org/W2002850650","https://openalex.org/W2092244978","https://openalex.org/W3045508281","https://openalex.org/W2065141842","https://openalex.org/W1995461348","https://openalex.org/W2076847960","https://openalex.org/W1493691865"],"abstract_inverted_index":{"Previous":[0,433],"article":[1,3,434,436],"Next":[2,435],"Generalized":[4,55,84,412,461,492,529,538,570,573,581,599,610,613,621,640],"Monotone":[5,462,493,600,622,641],"Affine":[6,242],"MapsJean-Pierre":[7],"Crouzeix":[8,12,152],"and":[9,13,28,51,59,63,78,87,111,124,134,141,153,161,164,182,200,225,245,271,287,312,336,353,408,414,417,444,464,476,483,513,525,540,550,561,572,603,612,656,674,692],"Siegfried":[10,14,49,404],"SchaibleJean-Pierre":[11],"Schaiblehttps://doi.org/10.1137/S0895479895290978PDFBibTexSections":[15],"ToolsAdd":[16],"to":[17,35],"favoritesExport":[18],"CitationTrack":[19],"CitationsEmail":[20],"SectionsAboutAbstractIn":[21],"this":[22],"paper":[23],"we":[24],"derive":[25],"new":[26],"necessary":[27],"sufficient":[29],"conditions":[30],"for":[31,131,159,184,501,580,609,672,690],"an":[32,473],"afflne":[33],"map":[34,475],"be":[36],"quasimonotone":[37],"on":[38,505,558,631,653],"a":[39,222,628],"convex":[40],"set.[1]":[41],"Mordecai":[42],"Avriel,":[43],",":[44,48,52,79,125,154,288,309,313,354,409],"Walter":[45],"E.":[46,82],"Diewert,":[47],"Schaible":[50,311],"Israel":[53],"Zang,":[54],"concavity,":[56],"Mathematical":[57],"Concepts":[58],"Methods":[60],"in":[61,615],"Science":[62],"Engineering,":[64],"Vol.":[65,455,486,515,563,593],"36,":[66],"Plenum":[67],"Press,":[68],"New":[69,94,424],"York,":[70,95,425],"1988x+332":[71],"89e:90155":[72],"0679.90029":[73],"CrossrefGoogle":[74,119,149,194,368],"Scholar[2]":[75],"Adi":[76],"Ben-Israel":[77],"Thomas":[80],"N.":[81],"Greville,":[83],"inverses:":[85],"theory":[86],"applications,":[88],"Wiley-Interscience":[89],"[John":[90],"Wiley":[91],"&":[92,681],"Sons],":[93],"1974xi+395":[96],"53:469":[97],"0305.15001":[98],"Google":[99,383,430],"Scholar[3]":[100],"Richard":[101,121],"W.":[102,122],"Cottle,":[103],"Manifestations":[104],"of":[105,136,180,221,293,317,359,389,448,472,481,510,528,569,590,627,634],"the":[106,132,219,226,246,477,526,616,632,635],"Schur":[107],"complement,":[108],"Linear":[109,139,204,228,502,522,541,629],"Algebra":[110,140,205,229],"Appl.,":[112,142,206,230,254,277,299,324,396],"8":[113],"(1974),":[114],"189\u2013211":[115],"10.1016/0024-3795(74)90066-4":[116],"50:7204":[117],"0284.15005":[118],"Scholar[4]":[120],"Cottle":[123],"Jacques":[126,155,175],"A.":[127,156,176,410,546,548],"Ferland,":[128,157,177],"Matrix-theoretic":[129],"criteria":[130],"quasi-convexity":[133,181],"pseudo-convexity":[135,183],"quadratic":[137,185,337,391],"functions,":[138,186,392],"5":[143],"(1972),":[144,190],"123\u2013136":[145],"10.1016/0024-3795(72)90022-5":[146],"46:197":[147],"0241.90045":[148],"Scholar[5]":[150],"Jean-Pierre":[151],"Criteria":[158,579,608],"quasiconvexity":[160],"pseudoconvexity:":[162],"relationships":[163],"comparisons,":[165],"Math.":[166,187],"Programming,":[167,188,592],"23":[168],"(1982),":[169],"193\u2013205":[170],"83f:90106":[171],"0479.90067":[172],"CrossrefISIGoogle":[173,213,237,283,305,330,402],"Scholar[6]":[174],"Maximal":[178],"domains":[179],"3":[189,489,596],"178\u2013192":[191],"47:1834":[192],"0256.90040":[193],"Scholar[7]":[195],"M.":[196,215,239],"Seetharama":[197,216,240],"Gowda,":[198,217,241],"Pseudomonotone":[199,585],"copositive":[201],"star":[202],"matrices,":[203],"113":[207],"(1989),":[208],"107\u2013118":[209],"10.1016/0024-3795(89)90289-9":[210],"90c:90222":[211],"0661.15018":[212],"Scholar[8]":[214],"On":[218],"transpose":[220],"pseudomonotone":[223,243,272],"matrix":[224],"LCP,":[227],"140":[231],"(1990),":[232,256,301],"129\u2013137":[233],"10.1016/0024-3795(90)90225-2":[234],"92b:90213":[235],"0734.90099":[236],"Scholar[9]":[238],"mappings":[244],"linear":[247],"complementarity":[248],"problem,":[249],"SIAM":[250,339,556],"J.":[251,274,296,321,340,393],"Matrix":[252,559,654],"Anal.":[253],"11":[255],"373\u2013380":[257],"10.1137/0611026":[258],"91e:90120":[259],"0719.90083":[260],"LinkISIGoogle":[261,349],"Scholar[10]":[262],"S.":[263,285,289,307,310,355,370,385,551],"Karamardian,":[264,308],"Complementarity":[265,465,503,523,542],"problems":[266,420],"over":[267],"cones":[268],"with":[269],"monotone":[270,294,319],"maps,":[273,295,320],"Optimization":[275,394,484,511],"Theory":[276,298,323,395,512],"18":[278],"(1976),":[279],"445\u2013454":[280],"57:11765":[281],"0304.49026":[282],"Scholar[11]":[284],"Karamardian":[286],"Schaible,":[290,356,371,386,405],"Seven":[291],"kinds":[292],"Optim.":[297,322],"66":[300],"37\u201346":[302],"91e:26016":[303],"0679.90055":[304],"Scholar[12]":[306],"J.-P.":[314],"Crouzeix,":[315,545],"Characterizations":[316],"generalized":[318,360],"76":[325],"(1993),":[326],"399\u2013413":[327],"94h:47102":[328],"0792.90070":[329],"Scholar[13]":[331],"B\u00e9la":[332],"Martos,":[333],"Subdefinite":[334,531,536],"matrices":[335],"forms,":[338],"Appl.":[341],"Math.,":[342],"17":[343],"(1969),":[344],"1215\u20131223":[345],"10.1137/0117112":[346],"41:5057":[347],"0186.34201":[348],"Scholar[14]":[350],"R.":[351],"Pini":[352],"Invariance":[357],"properties":[358],"monotonicity,":[361],"Optimization,":[362,454],"28":[363],"(1994),":[364],"211\u2013222":[365],"95c:90090":[366],"0818.90111":[367],"Scholar[15]":[369],"Masters":[372],"Thesis,":[373],"Beitr\u00e4ge":[374],"zur":[375],"quasikonvexen":[376],"Programmierung,":[377],"Doctoral":[378],"Dissertation,":[379],"K\u00f6ln,":[380],"Germany,":[381],"1971":[382],"Scholar[16]":[384],"Second-order":[387],"characterizations":[388],"pseudoconvex":[390],"21":[397],"(1977),":[398],"15\u201326":[399],"55:5818":[400],"0326.26004":[401],"Scholar[17]":[403],"F.":[406],"Giannessi":[407],"Maugeri,":[411],"monotonicity\u2014concepts":[413],"usesVariational":[415],"inequalities":[416],"network":[418],"equilibrium":[419],"(Erice,":[421],"1994),":[422],"Plenum,":[423],"1995,":[426],"289\u2013299":[427],"97a:47115":[428],"0847.49013":[429],"ScholarKeywordsaffine":[431],"mapquasimonotonicitypseudomonotonicity":[432],"FiguresRelatedReferencesCited":[437],"byDetails":[438],"Equivalence":[439],"between":[440],"p":[441,445],"-cyclic":[442,446],"quasimonotonicity":[443],"monotonicity":[447],"affine":[449,474],"maps12":[450],"March":[451],"2014":[452],"|":[453,555],"64,":[456],"No.":[457,488,517,565,595],"7":[458],"Cross":[459,469,490,497,519,533,577,583,597,606,619,624,638,645],"Ref":[460,470,491,498,520,534,578,584,598,607,620,625,639,646],"Maps":[463,496,623,644],"Problems21":[466],"May":[467],"2011":[468],"Pseudomonotonicity":[471,626],"two":[478],"dimensional":[479],"caseJournal":[480],"Information":[482],"Sciences,":[485],"29,":[487],"Single":[494,642],"Valued":[495,643],"Existence":[499,589],"Theorems":[500],"Problems":[504,602],"Solid":[506],"Closed":[507],"Convex":[508],"ConesJournal":[509],"Applications,":[514,562],"126,":[516],"2":[518],"The":[521],"Problem":[524],"Class":[527],"Positive":[530,535,636],"Matrices":[532],"Matrices,":[537],"Monotonicity,":[539,574],"ProblemsJ.":[543],"P.":[544],"Hassouni,":[547],"Lahlou,":[549],"Schaible31":[552],"July":[553,665],"2006":[554,666],"Journal":[557,652],"Analysis":[560,655],"22,":[564],"1AbstractPDF":[566],"(190":[567],"KB)Characterizations":[568],"Convexity":[571,611],"A":[575],"Survey":[576],"Monotonicity":[582,614],"variational":[586],"inequality":[587],"problems:":[588],"solutionsMathematical":[591],"78,":[594],"Equilibrium":[601],"Variational":[604],"Inequalities":[605],"Differentiable":[617],"Case":[618],"Map":[630],"Interior":[633],"Orthant":[637],"Volume":[647],"17,":[648],"Issue":[649],"4|":[650],"1996SIAM":[651],"Applications":[657],"History":[658],"Submitted:21":[659],"August":[660],"1995Accepted:30":[661],"November":[662],"1995Published":[663],"online:31":[664],"InformationCopyright":[667],"\u00a9":[668,670],"1996":[669],"Society":[671],"Industrial":[673,691],"Applied":[675,693],"MathematicsKeywordsaffine":[676],"mapquasimonotonicitypseudomonotonicityMSC":[677],"codes90C3026B25PDF":[678],"Download":[679],"Article":[680],"Publication":[682],"DataArticle":[683],"DOI:10.1137/S0895479895290978Article":[684],"page":[685],"range:pp.":[686],"992-997ISSN":[687],"(print):0895-4798ISSN":[688],"(online):1095-7162Publisher:Society":[689],"Mathematics":[694]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}