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Set-Valued and Variational Analysis最新文献

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Regularity of Sets Under a Reformulation in a Product Space with Reduced Dimension 降维积空间重构下集合的正则性
IF 1.6 3区 数学
Set-Valued and Variational Analysis Pub Date : 2023-11-20 DOI: 10.1007/s11228-023-00702-2
Rubén Campoy
{"title":"Regularity of Sets Under a Reformulation in a Product Space with Reduced Dimension","authors":"Rubén Campoy","doi":"10.1007/s11228-023-00702-2","DOIUrl":"https://doi.org/10.1007/s11228-023-00702-2","url":null,"abstract":"<p>Different notions on regularity of sets and of collection of sets play an important role in the analysis of the convergence of projection algorithms in nonconvex scenarios. While some projection algorithms can be applied to feasibility problems defined by finitely many sets, some other require the use of a product space reformulation to construct equivalent problems with two sets. In this work we analyze how some regularity properties are preserved under a reformulation in a product space of reduced dimension. This allows us to establish local linear convergence of parallel projection methods which are constructed through this reformulation.</p>","PeriodicalId":49537,"journal":{"name":"Set-Valued and Variational Analysis","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138540743","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}
引用次数: 0
Correction to: Necessary Conditions in Infinite-Horizon Control Problems That Need No Asymptotic Assumptions 修正:不需要渐近假设的无限视界控制问题的必要条件
3区 数学
Set-Valued and Variational Analysis Pub Date : 2023-11-07 DOI: 10.1007/s11228-023-00699-8
Dmitry Khlopin
{"title":"Correction to: Necessary Conditions in Infinite-Horizon Control Problems That Need No Asymptotic Assumptions","authors":"Dmitry Khlopin","doi":"10.1007/s11228-023-00699-8","DOIUrl":"https://doi.org/10.1007/s11228-023-00699-8","url":null,"abstract":"","PeriodicalId":49537,"journal":{"name":"Set-Valued and Variational Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135480551","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}
引用次数: 0
A Strong Law of Large Numbers for Random Monotone Operators 随机单调算子的一个强大数定律
3区 数学
Set-Valued and Variational Analysis Pub Date : 2023-11-06 DOI: 10.1007/s11228-023-00701-3
Adil Salim
{"title":"A Strong Law of Large Numbers for Random Monotone Operators","authors":"Adil Salim","doi":"10.1007/s11228-023-00701-3","DOIUrl":"https://doi.org/10.1007/s11228-023-00701-3","url":null,"abstract":"","PeriodicalId":49537,"journal":{"name":"Set-Valued and Variational Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135544400","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}
引用次数: 1
Nonlinear Forward-Backward Splitting with Momentum Correction 具有动量校正的非线性前向后分裂
3区 数学
Set-Valued and Variational Analysis Pub Date : 2023-11-03 DOI: 10.1007/s11228-023-00700-4
Martin Morin, Sebastian Banert, Pontus Giselsson
{"title":"Nonlinear Forward-Backward Splitting with Momentum Correction","authors":"Martin Morin, Sebastian Banert, Pontus Giselsson","doi":"10.1007/s11228-023-00700-4","DOIUrl":"https://doi.org/10.1007/s11228-023-00700-4","url":null,"abstract":"Abstract The nonlinear, or warped, resolvent recently explored by Giselsson and Bùi-Combettes has been used to model a large set of existing and new monotone inclusion algorithms. To establish convergent algorithms based on these resolvents, corrective projection steps are utilized in both works. We present a different way of ensuring convergence by means of a nonlinear momentum term, which in many cases leads to cheaper per-iteration cost. The expressiveness of our method is demonstrated by deriving a wide range of special cases. These cases cover and expand on the forward-reflected-backward method of Malitsky-Tam, the primal-dual methods of Vũ-Condat and Chambolle-Pock, and the forward-reflected-Douglas-Rachford method of Ryu-Vũ. A new primal-dual method that uses an extra resolvent step is also presented as well as a general approach for adding momentum to any special case of our nonlinear forward-backward method, in particular all the algorithms listed above.","PeriodicalId":49537,"journal":{"name":"Set-Valued and Variational Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135775006","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}
引用次数: 6
Projectional Coderivatives and Calculus Rules 投影协导数与微积分规则
3区 数学
Set-Valued and Variational Analysis Pub Date : 2023-10-30 DOI: 10.1007/s11228-023-00698-9
Wenfang Yao, Kaiwen Meng, Minghua Li, Xiaoqi Yang
{"title":"Projectional Coderivatives and Calculus Rules","authors":"Wenfang Yao, Kaiwen Meng, Minghua Li, Xiaoqi Yang","doi":"10.1007/s11228-023-00698-9","DOIUrl":"https://doi.org/10.1007/s11228-023-00698-9","url":null,"abstract":"","PeriodicalId":49537,"journal":{"name":"Set-Valued and Variational Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136104479","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}
引用次数: 2
Caristi-Type Conditions in Constraint Minimisation of Mappings in Metric and Partially Ordered Spaces 度量和部分有序空间中映射约束极小化的caristi型条件
3区 数学
Set-Valued and Variational Analysis Pub Date : 2023-10-24 DOI: 10.1007/s11228-023-00697-w
Evgeny Zhukovskiy, Evgenii Burlakov, Ivan Malkov
{"title":"Caristi-Type Conditions in Constraint Minimisation of Mappings in Metric and Partially Ordered Spaces","authors":"Evgeny Zhukovskiy, Evgenii Burlakov, Ivan Malkov","doi":"10.1007/s11228-023-00697-w","DOIUrl":"https://doi.org/10.1007/s11228-023-00697-w","url":null,"abstract":"","PeriodicalId":49537,"journal":{"name":"Set-Valued and Variational Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135267435","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}
引用次数: 0
Singular Value Analysis of Linear Maps Under Conic Constraints 二次约束下线性映射的奇异值分析
3区 数学
Set-Valued and Variational Analysis Pub Date : 2023-09-19 DOI: 10.1007/s11228-023-00696-x
Alberto Seeger, David Sossa
{"title":"Singular Value Analysis of Linear Maps Under Conic Constraints","authors":"Alberto Seeger, David Sossa","doi":"10.1007/s11228-023-00696-x","DOIUrl":"https://doi.org/10.1007/s11228-023-00696-x","url":null,"abstract":"","PeriodicalId":49537,"journal":{"name":"Set-Valued and Variational Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135060633","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}
引用次数: 0
Viscous Approximations of Non-Convex Sweeping Processes in the Space of Regulated Functions 正则函数空间中非凸扫描过程的粘性逼近
3区 数学
Set-Valued and Variational Analysis Pub Date : 2023-09-19 DOI: 10.1007/s11228-023-00695-y
Pavel Krejčí, Giselle A. Monteiro, Vincenzo Recupero
{"title":"Viscous Approximations of Non-Convex Sweeping Processes in the Space of Regulated Functions","authors":"Pavel Krejčí, Giselle A. Monteiro, Vincenzo Recupero","doi":"10.1007/s11228-023-00695-y","DOIUrl":"https://doi.org/10.1007/s11228-023-00695-y","url":null,"abstract":"","PeriodicalId":49537,"journal":{"name":"Set-Valued and Variational Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135061228","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}
引用次数: 0
Viability and Filippov-type Lemma for Stieltjes Differential Inclusions Stieltjes微分包含的生存性和Filippov型引理
IF 1.6 3区 数学
Set-Valued and Variational Analysis Pub Date : 2023-09-01 DOI: 10.1007/s11228-023-00690-3
B. Satco, G. Smyrlis
{"title":"Viability and Filippov-type Lemma for Stieltjes Differential Inclusions","authors":"B. Satco, G. Smyrlis","doi":"10.1007/s11228-023-00690-3","DOIUrl":"https://doi.org/10.1007/s11228-023-00690-3","url":null,"abstract":"","PeriodicalId":49537,"journal":{"name":"Set-Valued and Variational Analysis","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46937484","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}
引用次数: 0
Nonlocal Error Bounds for Piecewise Affine Functions 分段仿射函数的非局部误差边界
3区 数学
Set-Valued and Variational Analysis Pub Date : 2023-09-01 DOI: 10.1007/s11228-023-00694-z
M. V. Dolgopolik
{"title":"Nonlocal Error Bounds for Piecewise Affine Functions","authors":"M. V. Dolgopolik","doi":"10.1007/s11228-023-00694-z","DOIUrl":"https://doi.org/10.1007/s11228-023-00694-z","url":null,"abstract":"","PeriodicalId":49537,"journal":{"name":"Set-Valued and Variational Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135304646","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}
引用次数: 0
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