Results 71 to 80 of about 2,299 (159)

Weakened subdifferentials and Frechet differentiability of real functions [PDF]

Let X be a real Banach space and f : X ! R [ {+1}. It is well known that the Clarke subdifferential @ f(x) of the function f at x 2 int dom f is a singleton if and only if f is strongly differentiable (then @ f(x) = {Dsf(x)}, where Dsf(x) is the strong ...
Ginchev Ivan
core  

The approximate and the Clarke subdifferentials can be different everywhere

Journal of Mathematical Analysis and Applications, 2008
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openaire   +1 more source

Optimality and scalarization of robust approximate solutions for semi-infinite vector equilibrium problems

Journal of Inequalities and Applications
This paper investigates the optimality conditions and scalarization theorems for robust approximate solutions to semi-infinite vector equilibrium problems with data uncertainty in the constraints.
Shan Cai, Xiaoping Li
doaj   +1 more source

Critical metrics of eigenvalue functionals via Clarke subdifferential

62 ...
Petrides, Romain, Tewodrose, David
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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   +2 more sources

Three nontrivial solutions for nonlocal anisotropic inclusions under nonresonance

Electronic Journal of Differential Equations, 2019
In this article, we study a pseudo-differential inclusion driven by a nonlocal anisotropic operator and a Clarke generalized subdifferential of a nonsmooth potential, which satisfies nonresonance conditions both at the origin and at infinity. We prove
Silvia Frassu, Eugenio M. Rocha, Vasile Staicu   +2 more
doaj  

Homological differential calculus

, 2019
This article provides a definition of a subdifferential for continuous functions based on homological considerations. We show that it satisfies all the requirement for a good notion of subdifferential.
Vichery, Nicolas
core  

Lagrange Duality and Saddle-Point Optimality Conditions for Nonsmooth Interval-Valued Multiobjective Semi-Infinite Programming Problems with Vanishing Constraints

Axioms
This article deals with a class of nonsmooth interval-valued multiobjective semi-infinite programming problems with vanishing constraints (NIMSIPVC). We introduce the VC-Abadie constraint qualification (VC-ACQ) for NIMSIPVC and employ it to establish ...
Balendu Bhooshan Upadhyay, Shivani Sain, Ioan Stancu-Minasian   +2 more
doaj   +1 more source

Unified Robust Necessary Optimality Conditions for Nonconvex Nonsmooth Uncertain Multiobjective Optimization. [PDF]

J Optim Theory Appl, 2022
Wang J, Li S, Feng M.
europepmc   +1 more source

A new class of dual systems of fractional differential equations with hemivariational inequalities

Journal of Inequalities and Applications
The main goal of this paper is to analyze and study a new class of dual abstract systems that consists of differential hemivariational inequalities systematized by an evolutionary hemivariational inequality accumulated with a fractional differential ...
Mohd Adnan, Esmail Alshaban, Fahad M. Alamrani, Abdur Raheem, Areefa Khatoon, Faizan A. Khan   +5 more
doaj   +1 more source