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Set-Valued and Variational Analysis最新文献

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On Diffeologies for Power Sets and Measures 论功率集与测度的微分
IF 1.6 3区 数学 Q2 MATHEMATICS, APPLIED
Set-Valued and Variational Analysis
Pub Date : 2023-11-21 DOI: 10.1007/s11228-023-00703-1
Alireza Ahmadi, Jean-Pierre Magnot

We consider a differential geometric setting on power sets and Borel algebras. Our chosen framework is based on diffeologies, and we make a link between the various diffeological structures that we propose, having in mind set-valued maps, relations, set-valued gradients, differentiable measures, and shape analysis. This work intends to establish rigorous properties on sample diffeologies that seem of interest to us.

考虑幂集和Borel代数上的微分几何集。我们选择的框架是基于微分学的，我们在我们提出的各种微分结构之间建立了联系，在脑海中有集值映射、关系、集值梯度、可微测度和形状分析。这项工作旨在建立我们感兴趣的样品微分学的严格性质。
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引用次数: 1
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 Q2 MATHEMATICS, APPLIED
Set-Valued and Variational Analysis
Pub Date : 2023-11-20 DOI: 10.1007/s11228-023-00702-2
Rubén Campoy

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.

关于集合的正则性和集合集合的正则性的不同概念在分析非凸情形下投影算法的收敛性时起着重要的作用。虽然一些投影算法可以应用于由有限多个集合定义的可行性问题，但其他一些则需要使用积空间重构来构造具有两个集合的等效问题。在本文中，我们分析了在降维积空间中，一些正则性是如何在重新表述下保持的。这允许我们建立局部线性收敛的平行投影方法，这是构造通过这个重新表述。
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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 Q2 MATHEMATICS, APPLIED
Set-Valued and Variational Analysis
Pub Date : 2023-11-07 DOI: 10.1007/s11228-023-00699-8
Dmitry Khlopin
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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 Q2 MATHEMATICS, APPLIED
Set-Valued and Variational Analysis
Pub Date : 2023-11-06 DOI: 10.1007/s11228-023-00701-3
Adil Salim
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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 Q2 MATHEMATICS, APPLIED
Set-Valued and Variational Analysis
Pub Date : 2023-11-03 DOI: 10.1007/s11228-023-00700-4
Martin Morin, Sebastian Banert, Pontus Giselsson
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.
Giselsson和Bùi-Combettes最近探索的非线性或翘曲解已经被用来模拟大量现有的和新的单调包含算法。为了建立基于这些解的收敛算法，在这两项工作中都使用了校正投影步骤。我们提出了一种利用非线性动量项来保证收敛性的不同方法，这种方法在许多情况下可以降低每次迭代的成本。通过推导一系列的特殊情况，证明了我们方法的表达性。这些案例涵盖并扩展了Malitsky-Tam的前向反射-后向方法、Vũ-Condat和Chambolle-Pock的原对偶方法以及ryu - vmu的前向反射- douglas - rachford方法。本文还提出了一种新的原始对偶方法，该方法使用了一个额外的解决步骤，以及一种一般的方法来增加动量到我们的非线性前向后向方法的任何特殊情况，特别是上面列出的所有算法。
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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 Q2 MATHEMATICS, APPLIED
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
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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 Q2 MATHEMATICS, APPLIED
Set-Valued and Variational Analysis
Pub Date : 2023-10-24 DOI: 10.1007/s11228-023-00697-w
Evgeny Zhukovskiy, Evgenii Burlakov, Ivan Malkov
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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 Q2 MATHEMATICS, APPLIED
Set-Valued and Variational Analysis
Pub Date : 2023-09-19 DOI: 10.1007/s11228-023-00696-x
Alberto Seeger, David Sossa
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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 Q2 MATHEMATICS, APPLIED
Set-Valued and Variational Analysis
Pub Date : 2023-09-19 DOI: 10.1007/s11228-023-00695-y
Pavel Krejčí, Giselle A. Monteiro, Vincenzo Recupero
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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 Q2 MATHEMATICS, APPLIED
Set-Valued and Variational Analysis
Pub Date : 2023-09-01 DOI: 10.1007/s11228-023-00690-3
B. Satco, G. Smyrlis
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引用次数: 0
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