Results 11 to 20 of about 351 (168)

Reconstruction of the Clarke Subdifferential by the Lasry–Lions Regularizations

Journal of Mathematical Analysis and Applications, 2000
Suppose that \(f\) is a locally Lipschitz function defined on a Hilbert space, which satisfies the growth condition \[ -{C\over 2}(\|x\|^2+ 1)\leq f(x)\leq {C\over 2}(\|x\|^2+ 1). \] It is proved that the Clarke subdifferential \(\partial f(x)\) (of \(f\) at \(x\)) can be represented by the derivatives of its Lasry-Lions regularizations \((f_\lambda ...
Georgiev, Pando Gr., Zlateva, Nadia P.
openaire   +3 more sources

Efficient Automatic Subdifferentiation for Programs with Linear Branches

Mathematics, 2023
Computing an element of the Clarke subdifferential of a function represented by a program is an important problem in modern non-smooth optimization.
Sejun Park
doaj   +2 more sources

On the Clarke subdifferential of the distance function of a closed set

Journal of Mathematical Analysis and Applications, 1992
The authors derive formulas for computing the Clarke subdifferential of the distance function \(x\in X\mapsto d_ C(x)=\text{Inf}\{\| x- y\|: y\in C\}\). In connection with this question, they examine the role of the dimensionality of \(X\), the convexity of \(C\), and the (subdifferential) regularity of \(d_ C\).
Burke, James V, Ferris, Michael C, Qian, Maijian   +2 more
openaire   +3 more sources

Existence trajectory and optimal control of Clarke subdifferential stochastic integrodifferential inclusions suffered by non-instantaneous impulses and deviated arguments

Results in Control and Optimization, 2023
In this article, the solvability, Trajectory(T-) and optimal controllability of stochastic integrodifferential inclusions with Clarke subdifferential along with deviated arguments and Poisson jumps are analyzed which are new and untreated topics in the ...
K. Ramkumar, K. Ravikumar, Dimplekumar Chalishajar   +2 more
doaj   +2 more sources

Existence of solutions for a second order boundary value problem with the Clarke subdifferential

Filomat, 2017
In this paper, we prove a theorem on the existence of solutions for a second order differential inclusion governed by the Clarke subdifferential of a Lipschitzian function and by a mixed semicontinuous perturbation.
Azzam-Laouir, Dalila, Melit, Samira
openaire   +2 more sources

Implicit Multifunction Theorems in Banach Spaces [PDF]

Journal of Applied Mathematics, 2014
This paper is mainly devoted to the study of implicit multifunction theorems in terms of Clarke coderivative in general Banach spaces. We present new sufficient conditions for the local metric regularity, metric regularity, Lipschitz-like property ...
Ming-ge Yang, Yi-fan Xu
doaj   +2 more sources

Convergence of a double step scheme for a class of second order Clarke subdifferential inclusions

Nonlinear Analysis: Real World Applications, 2023
In this paper we deal with a second order evolution inclusion involving a multivalued term generated by a Clarke subdifferential of a locally Lipschitz potential. For this problem we construct a double step time-semidiscrete approximation, known as the Rothe scheme.
Bartosz, Krzysztof, Szafraniec, Paweł
openaire   +6 more sources

Null Controllability of Hilfer Fractional Stochastic Differential Inclusions

Fractal and Fractional, 2022
This paper gives the null controllability for nonlocal stochastic differential inclusion with the Hilfer fractional derivative and Clarke subdifferential.
Hamdy M. Ahmed, Mahmoud M. El-Borai, Wagdy El-Sayed, Alaa Elbadrawi   +3 more
doaj   +1 more source

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, Aris Daniilidis, Marc Quincampoix   +2 more
openaire   +3 more sources

Trajectory controllability of Clarke subdifferential type Hilfer fractional stochastic differential inclusion with non-instantaneous impulsive effects and deviated argument

Results in Control and Optimization, 2023
This manuscript is devoted to analyse the solvability and trajectory controllability of Hilfer fractional non-instantaneous impulsive stochastic differential inclusion with Clarke subdifferential and deviated argument.
N. Durga, Muslim Malik
doaj   +1 more source