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Set-Valued and Variational Analysis最新文献

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Sensitivity Analysis in Parametric Convex Vector Optimization 参数凸向量优化中的灵敏度分析
IF 1.6 3区 数学
Set-Valued and Variational Analysis Pub Date : 2024-09-18 DOI: 10.1007/s11228-024-00733-3
Duong Thi Viet An, Le Thanh Tung
{"title":"Sensitivity Analysis in Parametric Convex Vector Optimization","authors":"Duong Thi Viet An, Le Thanh Tung","doi":"10.1007/s11228-024-00733-3","DOIUrl":"https://doi.org/10.1007/s11228-024-00733-3","url":null,"abstract":"<p>In this paper, sensitivity analysis of the efficient sets in parametric convex vector optimization is considered. Namely, the perturbation, weak perturbation, and proper perturbation maps are defined as set-valued maps. We establish the formulas for computing the Fréchet coderivative of the profile of the above three kinds of perturbation maps. Because of the convexity assumptions, the conditions set are fairly simple if compared to those in the general case. In addition, our conditions are stated directly on the data of the problem. It is worth emphasizing that our approach is based on convex analysis tools which are different from those in the general case.</p>","PeriodicalId":49537,"journal":{"name":"Set-Valued and Variational Analysis","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142263036","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
Steepest Geometric Descent for Regularized Quasiconvex Functions 正则化准凸函数的最陡几何下降法
IF 1.6 3区 数学
Set-Valued and Variational Analysis Pub Date : 2024-08-23 DOI: 10.1007/s11228-024-00731-5
Aris Daniilidis, David Salas
{"title":"Steepest Geometric Descent for Regularized Quasiconvex Functions","authors":"Aris Daniilidis, David Salas","doi":"10.1007/s11228-024-00731-5","DOIUrl":"https://doi.org/10.1007/s11228-024-00731-5","url":null,"abstract":"<p>We establish existence of steepest descent curves emanating from almost every point of a regular locally Lipschitz quasiconvex functions, where regularity means that the sweeping process flow induced by the sublevel sets is reversible. We then use max-convolution to regularize general quasiconvex functions and obtain a result of the same nature in a more general setting.</p>","PeriodicalId":49537,"journal":{"name":"Set-Valued and Variational Analysis","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142179534","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
On New Generalized Differentials with Respect to a Set and Their Applications 论关于集合的新广义微分及其应用
IF 1.6 3区 数学
Set-Valued and Variational Analysis Pub Date : 2024-08-14 DOI: 10.1007/s11228-024-00729-z
Xiaolong Qin, Vo Duc Thinh, Jen-Chih Yao
{"title":"On New Generalized Differentials with Respect to a Set and Their Applications","authors":"Xiaolong Qin, Vo Duc Thinh, Jen-Chih Yao","doi":"10.1007/s11228-024-00729-z","DOIUrl":"https://doi.org/10.1007/s11228-024-00729-z","url":null,"abstract":"<p>The notions and certain fundamental characteristics of the proximal and limiting normal cones with respect to a set are first presented in this paper. We present the ideas of the limiting coderivative and subdifferential with respect to a set of multifunctions and singleton mappings, respectively, based on these normal cones. The necessary and sufficient conditions for the Aubin property with respect to a set of multifunctions are then described by using the limiting coderivative with respect to a set. As a result of the limiting subdifferential with respect to a set, we offer the requisite optimality criteria for local solutions to optimization problems. In addition, we also provide examples to demonstrate the outcomes.</p>","PeriodicalId":49537,"journal":{"name":"Set-Valued and Variational Analysis","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142179536","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
Two New Splitting Methods for Three-Operator Monotone Inclusions in Hilbert Spaces 希尔伯特空间中三操作单调夹杂的两种新分割方法
IF 1.6 3区 数学
Set-Valued and Variational Analysis Pub Date : 2024-08-05 DOI: 10.1007/s11228-024-00730-6
Van Dung Nguyen, Nguyen The Vinh
{"title":"Two New Splitting Methods for Three-Operator Monotone Inclusions in Hilbert Spaces","authors":"Van Dung Nguyen, Nguyen The Vinh","doi":"10.1007/s11228-024-00730-6","DOIUrl":"https://doi.org/10.1007/s11228-024-00730-6","url":null,"abstract":"<p>In this paper, we propose two new unified splitting methods for monotone inclusion problems with three operators in real Hilbert spaces. These methods are based on the combination of Douglas-Rachford method and other methods, forward-backward-forward method and reflected-forward-backward method. The weak convergence of new algorithms under standard assumptions is established. We also give some numerical examples to demonstrate the efficiency of the proposed methods.</p>","PeriodicalId":49537,"journal":{"name":"Set-Valued and Variational Analysis","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141933782","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: Calmness of a Perturbed Cournot Oligopoly Game with Nonsmooth Cost Functions 更正：具有非光滑成本函数的扰动库诺寡头博弈的平静性
IF 1.3 3区 数学
Set-Valued and Variational Analysis Pub Date : 2024-07-16 DOI: 10.1007/s11228-024-00726-2
Matthieu Maréchal
{"title":"Correction to: Calmness of a Perturbed Cournot Oligopoly Game with Nonsmooth Cost Functions","authors":"Matthieu Maréchal","doi":"10.1007/s11228-024-00726-2","DOIUrl":"https://doi.org/10.1007/s11228-024-00726-2","url":null,"abstract":"","PeriodicalId":49537,"journal":{"name":"Set-Valued and Variational Analysis","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141643250","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
Lower Semicontinuity of Intersections of Set-Valued Maps and Applications on Bilevel Games 定值映射交集的下半连续性及其在双层游戏中的应用
IF 1.3 3区 数学
Set-Valued and Variational Analysis Pub Date : 2024-07-16 DOI: 10.1007/s11228-024-00728-0
Anton Svensson
{"title":"Lower Semicontinuity of Intersections of Set-Valued Maps and Applications on Bilevel Games","authors":"Anton Svensson","doi":"10.1007/s11228-024-00728-0","DOIUrl":"https://doi.org/10.1007/s11228-024-00728-0","url":null,"abstract":"","PeriodicalId":49537,"journal":{"name":"Set-Valued and Variational Analysis","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141640638","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
Subtransversality and Strong CHIP of Closed Sets in Asplund Spaces 阿斯普朗德空间中封闭集的次横向性和强CHIP
IF 1.3 3区 数学
Set-Valued and Variational Analysis Pub Date : 2024-07-15 DOI: 10.1007/s11228-024-00727-1
Zhou Wei, M. Théra, Jen-Chih Yao
{"title":"Subtransversality and Strong CHIP of Closed Sets in Asplund Spaces","authors":"Zhou Wei, M. Théra, Jen-Chih Yao","doi":"10.1007/s11228-024-00727-1","DOIUrl":"https://doi.org/10.1007/s11228-024-00727-1","url":null,"abstract":"","PeriodicalId":49537,"journal":{"name":"Set-Valued and Variational Analysis","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141647283","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
Sequential M-Stationarity Conditions for General Optimization Problems 一般优化问题的顺序 M 静态条件
IF 1.6 3区 数学
Set-Valued and Variational Analysis Pub Date : 2024-06-19 DOI: 10.1007/s11228-024-00724-4
Nooshin Movahedian, Fatemeh Pourahmad
{"title":"Sequential M-Stationarity Conditions for General Optimization Problems","authors":"Nooshin Movahedian, Fatemeh Pourahmad","doi":"10.1007/s11228-024-00724-4","DOIUrl":"https://doi.org/10.1007/s11228-024-00724-4","url":null,"abstract":"<p>In this paper, we investigate sequential M-stationarity conditions for a class of nonsmooth nonconvex general optimization problems. We introduce various types of such conditions and compare them with previously established conditions in smooth or convex cases. The application of the derived results is demonstrated in the context of nonsmooth sparsity-constrained optimization problems. Additionally, we devise a Lagrangian-type algorithm for a specific case of smooth sparsity problems. Several examples are presented throughout the paper to illustrate the results.</p>","PeriodicalId":49537,"journal":{"name":"Set-Valued and Variational Analysis","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141546529","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
Approximation of Chattering Arcs in Optimal Control Problems Governed by Mono-Input Affine Control Systems 单输入仿射控制系统优化控制问题中喋喋弧的近似值
IF 1.6 3区 数学
Set-Valued and Variational Analysis Pub Date : 2024-06-17 DOI: 10.1007/s11228-024-00725-3
Térence Bayen, Francis Mairet
{"title":"Approximation of Chattering Arcs in Optimal Control Problems Governed by Mono-Input Affine Control Systems","authors":"Térence Bayen, Francis Mairet","doi":"10.1007/s11228-024-00725-3","DOIUrl":"https://doi.org/10.1007/s11228-024-00725-3","url":null,"abstract":"<p>In this paper, we consider a general Mayer optimal control problem governed by a mono-input affine control system whose optimal solution involves a second-order singular arc (leading to chattering). The objective of the paper is to present a numerical scheme to approach the chattering control by controls with a simpler structure (concatenation of bang-bang controls with a finite number of switching times and first-order singular arcs). Doing so, we consider a sequence of vector fields converging to the drift such that the associated optimal control problems involve only first-order singular arcs (and thus, optimal controls necessarily have a finite number of bang arcs). Up to a subsequence, we prove convergence of the sequence of extremals to an extremal of the original optimal control problem as well as convergence of the value functions. Next, we consider several examples of problems involving chattering. For each of them, we give an explicit family of approximated optimal control problems whose solutions involve bang arcs and first-order singular arcs. This allows us to approximate numerically solutions (with chattering) to these original optimal control problems.</p>","PeriodicalId":49537,"journal":{"name":"Set-Valued and Variational Analysis","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141546530","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
Generalized Nash Equilibrium from a Robustness Perspective in Variational Analysis 从变量分析的稳健性角度看广义纳什均衡
IF 1.6 3区 数学
Set-Valued and Variational Analysis Pub Date : 2024-06-01 DOI: 10.1007/s11228-024-00722-6
R. T. Rockafellar
{"title":"Generalized Nash Equilibrium from a Robustness Perspective in Variational Analysis","authors":"R. T. Rockafellar","doi":"10.1007/s11228-024-00722-6","DOIUrl":"https://doi.org/10.1007/s11228-024-00722-6","url":null,"abstract":"","PeriodicalId":49537,"journal":{"name":"Set-Valued and Variational Analysis","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141400873","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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