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Set-Valued and Variational Analysis最新文献

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Measure Differential Equations with a General Nonlocal Condition 具有一般非局部条件的量纲微分方程
IF 1.6 3区 数学
Set-Valued and Variational Analysis Pub Date : 2024-06-01 DOI: 10.1007/s11228-024-00723-5
Claudio A. Gallegos
{"title":"Measure Differential Equations with a General Nonlocal Condition","authors":"Claudio A. Gallegos","doi":"10.1007/s11228-024-00723-5","DOIUrl":"https://doi.org/10.1007/s11228-024-00723-5","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":"141410596","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
Sensitivity Analysis of the Set of Sustainable Thresholds 一组可持续阈值的敏感性分析
IF 1.6 3区 数学
Set-Valued and Variational Analysis Pub Date : 2024-05-29 DOI: 10.1007/s11228-024-00721-7
Pedro Gajardo, Thomas Guilmeau, Cristopher Hermosilla
{"title":"Sensitivity Analysis of the Set of Sustainable Thresholds","authors":"Pedro Gajardo, Thomas Guilmeau, Cristopher Hermosilla","doi":"10.1007/s11228-024-00721-7","DOIUrl":"https://doi.org/10.1007/s11228-024-00721-7","url":null,"abstract":"<p>In the context of constrained control-systems, the Set of Sustainable Thresholds plays in a sense the role of a dual object to the so-called Viability Kernel, because it describes all the thresholds that must be satisfied by the state of the system along a time interval, for a prescribed initial condition. This work aims at analyzing the sensitivity of the Set of Sustainable Thresholds, when it is seen as a set-valued map that depends on the initial position. In this regard, we investigate semicontinuity and Lipschitz continuity properties of this mapping, and we also study several contexts when the Set of Sustainable Thresholds is convex-valued.</p>","PeriodicalId":49537,"journal":{"name":"Set-Valued and Variational Analysis","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141165812","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
Complexity Analysis Based on Tuning the Viscosity Parameter of the Su-Boyd-Candès Inertial Gradient Dynamics 基于调整苏波依德-康德斯惯性梯度动力学粘度参数的复杂性分析
IF 1.6 3区 数学
Set-Valued and Variational Analysis Pub Date : 2024-05-21 DOI: 10.1007/s11228-024-00720-8
Samir Adly, H. Attouch
{"title":"Complexity Analysis Based on Tuning the Viscosity Parameter of the Su-Boyd-Candès Inertial Gradient Dynamics","authors":"Samir Adly, H. Attouch","doi":"10.1007/s11228-024-00720-8","DOIUrl":"https://doi.org/10.1007/s11228-024-00720-8","url":null,"abstract":"","PeriodicalId":49537,"journal":{"name":"Set-Valued and Variational Analysis","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141113210","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
Forward-Backward Algorithm for Functions with Locally Lipschitz Gradient: Applications to Mean Field Games 具有局部 Lipschitz 梯度的函数的前向-后向算法：均值场博弈的应用
IF 1.6 3区 数学
Set-Valued and Variational Analysis Pub Date : 2024-05-21 DOI: 10.1007/s11228-024-00719-1
Luis M. Briceño-Arias, Francisco J. Silva, Xianjin Yang
{"title":"Forward-Backward Algorithm for Functions with Locally Lipschitz Gradient: Applications to Mean Field Games","authors":"Luis M. Briceño-Arias, Francisco J. Silva, Xianjin Yang","doi":"10.1007/s11228-024-00719-1","DOIUrl":"https://doi.org/10.1007/s11228-024-00719-1","url":null,"abstract":"<p>In this paper, we provide a generalization of the forward-backward splitting algorithm for minimizing the sum of a proper convex lower semicontinuous function and a differentiable convex function whose gradient satisfies a locally Lipschitz-type condition. We prove the convergence of our method and derive a linear convergence rate when the differentiable function is locally strongly convex. We recover classical results in the case when the gradient of the differentiable function is globally Lipschitz continuous and an already known linear convergence rate when the function is globally strongly convex. We apply the algorithm to approximate equilibria of variational mean field game systems with local couplings. Compared with some benchmark algorithms to solve these problems, our numerical tests show similar performances in terms of the number of iterations but an important gain in the required computational time.</p>","PeriodicalId":49537,"journal":{"name":"Set-Valued and Variational Analysis","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141153388","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
Linear Convergence of the Derivative-Free Proximal Bundle Method on Convex Nonsmooth Functions, with Application to the Derivative-Free $mathcal{VU}$-Algorithm 凸非光滑函数上的无衍生近端束方法的线性收敛，以及对无衍生 $mathcal{VU}$算法的应用
IF 1.6 3区 数学
Set-Valued and Variational Analysis Pub Date : 2024-05-20 DOI: 10.1007/s11228-024-00718-2
C. Planiden, T. Rajapaksha
{"title":"Linear Convergence of the Derivative-Free Proximal Bundle Method on Convex Nonsmooth Functions, with Application to the Derivative-Free $mathcal{VU}$-Algorithm","authors":"C. Planiden, T. Rajapaksha","doi":"10.1007/s11228-024-00718-2","DOIUrl":"https://doi.org/10.1007/s11228-024-00718-2","url":null,"abstract":"","PeriodicalId":49537,"journal":{"name":"Set-Valued and Variational Analysis","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141120412","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 Quasi-Variational-Hemivariational Inequality for Incompressible Navier-Stokes System with Bingham Fluid 具有宾汉流体的不可压缩纳维-斯托克斯系统的准变量-半变量不等式
IF 1.6 3区 数学
Set-Valued and Variational Analysis Pub Date : 2024-05-15 DOI: 10.1007/s11228-024-00717-3
Stanisław Migórski, Sylwia Dudek
{"title":"A Quasi-Variational-Hemivariational Inequality for Incompressible Navier-Stokes System with Bingham Fluid","authors":"Stanisław Migórski, Sylwia Dudek","doi":"10.1007/s11228-024-00717-3","DOIUrl":"https://doi.org/10.1007/s11228-024-00717-3","url":null,"abstract":"","PeriodicalId":49537,"journal":{"name":"Set-Valued and Variational Analysis","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140977891","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
Stability for Parametric Control Problems of PDEs via Generalized Differentiation 通过广义微分求 PDE 参数控制问题的稳定性
IF 1.6 3区 数学
Set-Valued and Variational Analysis Pub Date : 2024-05-03 DOI: 10.1007/s11228-024-00716-4
N. T. Qui, P.-D. Le Thi
{"title":"Stability for Parametric Control Problems of PDEs via Generalized Differentiation","authors":"N. T. Qui, P.-D. Le Thi","doi":"10.1007/s11228-024-00716-4","DOIUrl":"https://doi.org/10.1007/s11228-024-00716-4","url":null,"abstract":"<p>This paper investigates the mathematical programming formulation of semilinear elliptic optimal control problems with finitely many state constraints, this allows the use of results in parametric mathematical programming. By applying recent stability results in parametric mathematical programming, we will obtain some new results on differential stability and tilt stability for parametric control problems. On the one hand, we derive an explicit upper estimate for regular subdifferential of marginal function of control problems under basic parameter perturbations. On the other hand, we establish a characterization of tilt stability of control problems under tilt parameter perturbations.</p>","PeriodicalId":49537,"journal":{"name":"Set-Valued and Variational Analysis","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140887676","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
Perturbation Method in Orlicz Sequence Spaces 奥利兹序列空间中的扰动法
IF 1.6 3区 数学
Set-Valued and Variational Analysis Pub Date : 2024-04-02 DOI: 10.1007/s11228-024-00715-5
{"title":"Perturbation Method in Orlicz Sequence Spaces","authors":"","doi":"10.1007/s11228-024-00715-5","DOIUrl":"https://doi.org/10.1007/s11228-024-00715-5","url":null,"abstract":"<h3>Abstract</h3> <p>We develop a new perturbation method in Orlicz sequence spaces <span> <span>(ell _{M})</span> </span> with Orlicz function <span> <span>(M)</span> </span> satisfying <span> <span>(Delta _{2})</span> </span> condition at zero. This result allows one to support from below any bounded below lower semicontinuous function with bounded support, with a perturbation of the defining function <span> <span>(sigma _{M})</span> </span>.</p> <p>We give few examples how the method can be used for determining the type of the smoothness of certain Orlicz spaces.</p>","PeriodicalId":49537,"journal":{"name":"Set-Valued and Variational Analysis","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140583108","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
Uniform Continuity of Multifunctions 多重函数的均匀连续性
IF 1.6 3区 数学
Set-Valued and Variational Analysis Pub Date : 2024-03-29 DOI: 10.1007/s11228-024-00714-6
M. Aggarwal
{"title":"Uniform Continuity of Multifunctions","authors":"M. Aggarwal","doi":"10.1007/s11228-024-00714-6","DOIUrl":"https://doi.org/10.1007/s11228-024-00714-6","url":null,"abstract":"","PeriodicalId":49537,"journal":{"name":"Set-Valued and Variational Analysis","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140368223","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
Inertial Krasnoselskii-Mann Iterations 惯性 Krasnoselskii-Mann 迭代
IF 1.6 3区 数学
Set-Valued and Variational Analysis Pub Date : 2024-03-26 DOI: 10.1007/s11228-024-00713-7
Juan José Maulén, Ignacio Fierro, Juan Peypouquet
{"title":"Inertial Krasnoselskii-Mann Iterations","authors":"Juan José Maulén, Ignacio Fierro, Juan Peypouquet","doi":"10.1007/s11228-024-00713-7","DOIUrl":"https://doi.org/10.1007/s11228-024-00713-7","url":null,"abstract":"<p>We establish the weak convergence of inertial Krasnoselskii-Mann iterations towards a common fixed point of a family of quasi-nonexpansive operators, along with estimates for the non-asymptotic rate at which the residuals vanish. Strong and linear convergence are obtained in the quasi-contractive setting. In both cases, we highlight the relationship with the non-inertial case, and show that passing from one regime to the other is a continuous process in terms of the hypotheses on the parameters. Numerical illustrations are provided for an inertial primal-dual method and an inertial three-operator splitting algorithm, whose performance is superior to that of their non-inertial counterparts.</p>","PeriodicalId":49537,"journal":{"name":"Set-Valued and Variational Analysis","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140298514","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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