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Linear Structure of Functions With Maximal Clarke Subdifferential [PDF]
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 $\ell^{\infty}(\mathbb{N})$).
Gonzalo Flores, Aris Daniilidis
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Evolution Inclusions With Clarke Subdifferential Type in Hilbert Space
The authors consider the existence of solutions for differential inclusions of the form \[ \begin{aligned} -\dot{x}(t) &\in \partial _{C}\phi (x(t))+G(t,x(t)),\\ x(0) &=x_0\end{aligned}\tag{1} \] in a real, separable Hilbert space \(H\), where \(\partial _{C}\) denotes the Clarke subdifferential.
Sitian Qin
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Existence and Controllability for Fractional Evolution Inclusions of Clarke’s Subdifferential Type
Applied Mathematics and Computation, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhenhai Liu, Biao Zeng
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AbstractIn this paper, Sobolev-type conformable fractional stochastic evolution inclusions with Clarke subdifferential and nonlocal conditions are studied. By using fractional calculus, stochastic analysis, properties of Clarke subdifferential and nonsmooth analysis, sufficient conditions for nonlocal controllability for the considered problem are ...
Maria Alessandra Ragusa, Hamdy M Ahmed
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Approximate Controllability for Stochastic Evolution Inclusions of Clarke’s Subdifferential Type
Applied Mathematics and Computation, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhenhai Liu, Maojun Bin, Liang Lu
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhenhai Liu +2 more
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Clarke Subdifferential for Lipschitzian Multivalued Mappings
Cybernetics and Systems Analysis, 1992zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The Clarke and Michel-Penot Subdifferentials of the Eigenvalues of a Symmetric Matrix
Computational Optimization and Applications, 1999zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jean-Baptiste Hiriart-Urruty +1 more
openaire +2 more sources
Applied Mathematics and Optimization, 2021
In this paper, the author studies the time optimal control of Clarke subdifferential type stochastic evolution inclusions with delay and non-instantaneous impulses of the form \[ d[x(t)-G(t,x_{t})] \in A(t)[x(t)-G(t,x_{t})]dt+B(t)u(t)dt+\partial F(t,x_{t})dw(t) t\in (s_{i},t_{i+1}], i=0,1,\dots,N,\] \[ x(t)\in g_{i}(t,x_{t}), t\in(t_{i},s_{i}], i=1 ...
Zuomao Yan
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In this paper, the author studies the time optimal control of Clarke subdifferential type stochastic evolution inclusions with delay and non-instantaneous impulses of the form \[ d[x(t)-G(t,x_{t})] \in A(t)[x(t)-G(t,x_{t})]dt+B(t)u(t)dt+\partial F(t,x_{t})dw(t) t\in (s_{i},t_{i+1}], i=0,1,\dots,N,\] \[ x(t)\in g_{i}(t,x_{t}), t\in(t_{i},s_{i}], i=1 ...
Zuomao Yan
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Representation of the Clarke Subdifferential for a Regular Quasidifferentiable Function
Journal of Optimization Theory and Applications, 1995zbMATH Open Web Interface contents unavailable due to conflicting licenses.
V F Demyanov
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