Pub Date : 2022-05-18DOI: 10.1007/s11228-022-00641-4
Ahmed Roubi
In this paper we deal with theorems of the alternative for systems of inequalities. Precisely, we give a formulation that encompasses several known alternative theorems and unifies their treatment under a minimax equality assumption which is fulfilled by a whole panoply of families of functions. We also give extensions of Yuan’s lemma to systems with several general functions provided that they fulfill a certain minimax theorem, and to some particular systems of several quadratic functions.
{"title":"Theorems of the Alternative Revisited and Some Extensions of Yuan’s Lemma","authors":"Ahmed Roubi","doi":"10.1007/s11228-022-00641-4","DOIUrl":"https://doi.org/10.1007/s11228-022-00641-4","url":null,"abstract":"<p>In this paper we deal with theorems of the alternative for systems of inequalities. Precisely, we give a formulation that encompasses several known alternative theorems and unifies their treatment under a minimax equality assumption which is fulfilled by a whole panoply of families of functions. We also give extensions of Yuan’s lemma to systems with several general functions provided that they fulfill a certain minimax theorem, and to some particular systems of several quadratic functions.</p>","PeriodicalId":49537,"journal":{"name":"Set-Valued and Variational Analysis","volume":"208 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2022-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138540766","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-05-06DOI: 10.1007/s11228-022-00640-5
M. Fabian, J. Hiriart-Urruty, E. Pauwels
{"title":"On the Generalized Jacobian of the Inverse of a Lipschitzian Mapping","authors":"M. Fabian, J. Hiriart-Urruty, E. Pauwels","doi":"10.1007/s11228-022-00640-5","DOIUrl":"https://doi.org/10.1007/s11228-022-00640-5","url":null,"abstract":"","PeriodicalId":49537,"journal":{"name":"Set-Valued and Variational Analysis","volume":"30 1","pages":"1443 - 1451"},"PeriodicalIF":1.6,"publicationDate":"2022-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43158615","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-04-21DOI: 10.1007/s11228-023-00683-2
Mengwei Xu, J. Ye
{"title":"Relaxed Constant Positive Linear Dependence Constraint Qualification for Disjunctive Systems","authors":"Mengwei Xu, J. Ye","doi":"10.1007/s11228-023-00683-2","DOIUrl":"https://doi.org/10.1007/s11228-023-00683-2","url":null,"abstract":"","PeriodicalId":49537,"journal":{"name":"Set-Valued and Variational Analysis","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2022-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44482783","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-04-05DOI: 10.1007/s11228-022-00632-5
J. Penot
{"title":"What is a Lipschitzian Manifold?","authors":"J. Penot","doi":"10.1007/s11228-022-00632-5","DOIUrl":"https://doi.org/10.1007/s11228-022-00632-5","url":null,"abstract":"","PeriodicalId":49537,"journal":{"name":"Set-Valued and Variational Analysis","volume":"30 1","pages":"1031 - 1040"},"PeriodicalIF":1.6,"publicationDate":"2022-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42758590","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-04-01DOI: 10.1007/s11228-022-00634-3
M. Balashov
{"title":"Stability of Minimization Problems and the Error Bound Condition","authors":"M. Balashov","doi":"10.1007/s11228-022-00634-3","DOIUrl":"https://doi.org/10.1007/s11228-022-00634-3","url":null,"abstract":"","PeriodicalId":49537,"journal":{"name":"Set-Valued and Variational Analysis","volume":"30 1","pages":"1061 - 1076"},"PeriodicalIF":1.6,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47458694","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-03-23DOI: 10.1007/s11228-022-00633-4
S. Apostolov, Mira Bivas, N. Ribarska
{"title":"Characterizations of Some Transversality-Type Properties","authors":"S. Apostolov, Mira Bivas, N. Ribarska","doi":"10.1007/s11228-022-00633-4","DOIUrl":"https://doi.org/10.1007/s11228-022-00633-4","url":null,"abstract":"","PeriodicalId":49537,"journal":{"name":"Set-Valued and Variational Analysis","volume":"30 1","pages":"1041 - 1060"},"PeriodicalIF":1.6,"publicationDate":"2022-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44390959","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-03-06DOI: 10.1007/s11228-022-00635-2
Y. Censor, E. Levy
{"title":"Limits of Eventual Families of Sets with Application to Algorithms for the Common Fixed Point Problem","authors":"Y. Censor, E. Levy","doi":"10.1007/s11228-022-00635-2","DOIUrl":"https://doi.org/10.1007/s11228-022-00635-2","url":null,"abstract":"","PeriodicalId":49537,"journal":{"name":"Set-Valued and Variational Analysis","volume":"30 1","pages":"1077 - 1088"},"PeriodicalIF":1.6,"publicationDate":"2022-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48280487","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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