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Linear Structure of Functions With Maximal Clarke Subdifferential [PDF]

open access: yesSIAM 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 $\ell^{\infty}(\mathbb{N})$).
Gonzalo Flores, Aris Daniilidis
exaly   +7 more sources

Evolution Inclusions With Clarke Subdifferential Type in Hilbert Space

open access: yesMathematical and Computer Modelling, 2010
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
exaly   +2 more sources
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Existence and Controllability for Fractional Evolution Inclusions of Clarke’s Subdifferential Type

Applied Mathematics and Computation, 2015
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhenhai Liu, Biao Zeng
exaly   +3 more sources

Nonlocal Controllability of Sobolev-Type Conformable Fractional Stochastic Evolution Inclusions With Clarke Subdifferential

open access: yesBulletin of the Malaysian Mathematical Sciences Society, 2022
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
exaly   +3 more sources

Approximate Controllability for Stochastic Evolution Inclusions of Clarke’s Subdifferential Type

Applied Mathematics and Computation, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhenhai Liu, Maojun Bin, Liang Lu
exaly   +3 more sources

Optimal Feedback Control and Controllability for Hyperbolic Evolution Inclusions of Clarke’s Subdifferential Type

open access: yesComputers and Mathematics With Applications, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhenhai Liu   +2 more
exaly   +5 more sources

Clarke Subdifferential for Lipschitzian Multivalued Mappings

Cybernetics and Systems Analysis, 1992
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
exaly   +2 more sources

The Clarke and Michel-Penot Subdifferentials of the Eigenvalues of a Symmetric Matrix

Computational Optimization and Applications, 1999
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jean-Baptiste Hiriart-Urruty   +1 more
openaire   +2 more sources

Time Optimal Control of a Clarke Subdifferential Type Stochastic Evolution Inclusion in Hilbert Spaces

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
exaly   +3 more sources

Representation of the Clarke Subdifferential for a Regular Quasidifferentiable Function

Journal of Optimization Theory and Applications, 1995
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V F Demyanov
exaly   +3 more sources

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