Results 71 to 80 of about 351 (168)

All convex bodies are in the subdifferential of some everywhere differentiable locally Lipschitz function

Proceedings of the London Mathematical Society, Volume 129, Issue 5, November 2024.
Abstract We construct a differentiable locally Lipschitz function f$f$ in RN$\mathbb {R}^{N}$ with the property that for every convex body K⊂RN$K\subset \mathbb {R}^N$ there exists x¯∈RN$\bar{x} \in \mathbb {R}^N$ such that K$K$ coincides with the set ∂Lf(x¯)$\partial _L f(\bar{x})$ of limits of derivatives {Df(xn)}n⩾1$\lbrace Df(x_n)\rbrace _{n ...
Aris Daniilidis, Robert Deville, Sebastián Tapia‐García   +2 more
wiley   +1 more source

Characterization of the Clarke regularity of subanalytic sets [PDF]

, 2017
International audienceIn this note, we will show that for a closed subanalytic subset $A \subset \mathbb{R}^n$, the Clarke tangential regularity of $A$ at $x_0 \in A$ is equivalent to the coincidence of the Clarke's tangent cone to $A$ at $x_0$ with ...
Abderrahim Jourani, Moustapha Séne, Séne, Moustapha, Jourani, Abderrahim   +3 more
core   +1 more source

Existence and optimal control results for Caputo fractional delay Clark's subdifferential inclusions of order r∈(1,2) with sectorial operators

Optimal Control Applications and Methods, Volume 45, Issue 4, Page 1832-1850, July/August 2024.
The graphical abstract delves into Caputo fractional nonlinear differential inclusions, highlighting their complexities and the need for innovative solutions. We propose a mild solution approach to address these challenges efficiently. Our investigation focuses on determining the existence of mild solutions under varied conditions and exploring optimal
Marimuthu Mohan Raja, Velusamy Vijayakumar, Kalyana Chakravarthy Veluvolu, Anurag Shukla, Kottakkaran Sooppy Nisar   +4 more
wiley   +1 more source

Subdifferential inclusions for stress formulations of unilateral contact problems [PDF]

, 2017
We consider two classes of inclusions involving subdifferential operators, both in the sense of Clarke and in the sense of convex analysis. An inclusion that belongs to the first class is stationary while an inclusion that belongs to the second class is
Sofonea, Mircea, Mircea Sofonea, Krzysztof Bartosz, Bartosz, Krzysztof   +3 more
core   +1 more source

A Neural Network Based on a Nonsmooth Equation for a Box Constrained Variational Inequality Problem

Journal of Mathematics, Volume 2024, Issue 1, 2024.
The variational inequality framework holds significant prominence across various domains including economic finance, network transportation, and game theory. In addition, a novel approach utilizing a neural network model is introduced in the current work to address a box constrained variational inequality problem.
Yanan Wang, Shuang Lin, Jie Zhang, Chen Qiu, B. B. Upadhyay   +4 more
wiley   +1 more source

A Nonconvex Proximal Bundle Method for Nonsmooth Constrained Optimization

Complexity, Volume 2024, Issue 1, 2024.
An implementable algorithm for solving nonsmooth nonconvex constrained optimization is proposed by combining bundle ideas, proximity control, and the exact penalty function. We construct two kinds of approximations to nonconvex objective function; these two approximations correspond to the convex and concave behaviors of the objective function at the ...
Jie Shen, Fang-Fang Guo, Na Xu, Sigurdur F. Hafstein   +3 more
wiley   +1 more source

Infinitely many solutions for an anisotropic differential inclusion on unbounded domains

Electronic Journal of Qualitative Theory of Differential Equations
The problem deals with the anisotropic $p(x)$-Laplacian operator where $p_i$ are Lipschitz continuous functions $2\leq p_i(x)
Giovany Figueiredo, Abdolrahman Razani
doaj   +1 more source

Subdifferential characterization of quasiconvexity and convexity [PDF]

, 1994
International audienceLet f : X → R ∪ {+∞} be a lower semicontinuous function on a Banach space X. We show that f is quasiconvex if and only if its Clarke subdifferential ∂f is quasimonotone.
Lassonde, Marc, Aussel, Didier, Corvellec, Jean-Noël   +2 more
core   +2 more sources

Attractors for Navier-Stokes flows with multivalued and nonmonotone subdifferential boundary conditions [PDF]

, 2014
We consider two-dimensional nonstationary Navier–Stokes shear flow with multivalued and nonmonotone boundary conditions on a part of the boundary of the flow domain.
Kalita, Piotr, Łukaszewicz, Grzegorz
core   +1 more source

Singular points of order $k$ of Clarke regular and arbitrary functions [PDF]

, 1992
summary:Let $X$ be a separable Banach space and $f$ a locally Lipschitz real function on $X$. For $k\in \mathbb N$, let $\Sigma_k(f)$ be the set of points $x\in X$, at which the Clarke subdifferential $\partial^Cf(x)$ is at least $k$-dimensional.
Alberti G, AMBROSIO, Luigi, AMBROSIO L., CANNARSA P., Zajíček, Luděk, ALBERTI, GIOVANNI   +5 more
core   +1 more source