Results 11 to 20 of about 2,296 (157)
Controllability and constrained controllability for nonlocal Hilfer fractional differential systems with Clarke’s subdifferential [PDF]
Journal of Inequalities and Applications, 2019 Sobolev-type nonlocal fractional differential systems with Clarke’s subdifferential are studied. Sufficient conditions for controllability and constrained controllability for Sobolev-type nonlocal fractional differential systems with Clarke’s ...
Hamdy M. Ahmed +3 more
doaj +3 more sources
On Clarke's Subdifferential of Marginal Functions [PDF]
Applied Set-Valued Analysis and Optimization, 2021 In this short note, we derive an upper estimate of Clarke's subdifferential of marginal functions in Banach spaces. The structure of the upper estimate is very similar to other results already obtained in the literature. The novelty lies on the fact that we derive our assertions in general Banach spaces, and avoid the use of the Asplund assumption.
Bouza, Gemayqzel +2 more
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Characterization of Filippov representable maps and Clarke subdifferentials [PDF]
Mathematical Programming, 2020 The ordinary differential equation $\dot{x}(t)=f(x(t)), \; t \geq 0 $, for $f$ measurable, is not sufficiently regular to guarantee existence of solutions. To remedy this we may relax the problem by replacing the function $f$ with its Filippov regularization $F_{f}$ and consider the differential inclusion $\dot{x}(t)\in F_{f}(x(t))$ which always has a ...
Mira Bivas +2 more
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Linear Structure of Functions with Maximal Clarke Subdifferential [PDF]
SIAM Journal on Optimization, 2019 It is hereby established that the set of Lipschitz functions $f:\mathcal{U}\rightarrow \mathbb{R}$ ($\mathcal{U}$ nonempty open subset of $\ell_{d}^{1}$) with maximal Clarke subdifferential contains a linear subspace of uncountable dimension (in particular, an isometric copy of $\ell^{\infty}(\mathbb{N})$).
Aris Daniilidis, Gonzalo Flores
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Lipschitz functions with maximal Clarke subdifferentials are staunch [PDF]
Bulletin of the Australian Mathematical Society, 2005 In a recent paper we have shown that most non-expansive Lipschitz functions (in the sense of Baire's category) have a maximal Clarke subdifferential. In the present paper, we show that in a separable Banach space the set of non-expansive Lipschitz functions with a maximal Clarke subdifferential is not only generic, but also staunch in the space of non ...
Borwein, Jonathan M., Wang, Xianfu
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Brittle membranes in finite elasticity
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Volume 103, Issue 11, November 2023., 2023 This work is devoted to the variational derivation of a reduced model for brittle membranes in finite elasticity. The main mathematical tools we develop for our analysis are: (i) a new density result in GSBVp$GSBV^{p}$ of functions satisfying a maximal‐rank constraint on the subgradients, which can be approximated by C1‐local immersions on regular ...
Stefano Almi +2 more
wiley +1 more source
Optimal allocations with α‐MaxMin utilities, Choquet expected utilities, and prospect theory
Theoretical Economics, Volume 18, Issue 3, Page 993-1022, July 2023., 2023 The analysis of optimal risk sharing has been thus far largely restricted to nonexpected utility models with concave utility functions, where concavity is an expression of ambiguity aversion and/or risk aversion. This paper extends the analysis to α‐maxmin expected utility, Choquet expected utility, and cumulative prospect theory, which accommodate ...
Patrick Beißner, Jan Werner
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Stat, Volume 11, Issue 1, December 2022., 2022 Recently, a special case of precision matrix estimation based on a distributionally robust optimization (DRO) framework has been shown to be equivalent to the graphical lasso. From this formulation, a method for choosing the regularization term, that is, for graphical model selection, was proposed.
Chau Tran +3 more
wiley +1 more source
Lipschitz functions with maximal Clarke subdifferentials are generic [PDF]
Proceedings of the American Mathematical Society, 2000 We show that on a separable Banach space most Lipschitz functions have maximal Clarke subdifferential mappings. In particular, the generic nonexpansive function has the dual unit ball as its Clarke subdifferential at every point. Diverse corollaries are given.
Borwein, Jonathan M., Wang, Xianfu
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Abstract and Applied Analysis, Volume 2022, Issue 1, 2022., 2022 In this paper, we establish a generalization of the Galewski‐Rădulescu nonsmooth global implicit function theorem to locally Lipschitz functions defined from infinite dimensional Banach spaces into Euclidean spaces. Moreover, we derive, under suitable conditions, a series of results on the existence, uniqueness, and possible continuity of global ...
Guy Degla +3 more
wiley +1 more source