Results 1 to 10 of about 7,741 (135)

Constrained nonsmooth problems of the calculus of variations

ESAIM: Control, Optimisation and Calculus of Variations, 2021
The paper is devoted to an analysis of optimality conditions for nonsmooth multidimensional problems of the calculus of variations with various types of constraints, such as additional constraints at the boundary and isoperimetric constraints. To derive optimality conditions, we study generalised concepts of differentiability of nonsmooth functions ...
Dolgopolik, M. V.
openaire   +4 more sources

Nonsmooth calculus [PDF]

Bulletin of the American Mathematical Society, 2007
We survey recent advances in analysis and geometry, where first order differential analysis has been extended beyond its classical smooth settings. Such studies have applications to geometric rigidity questions, but are also of intrinsic interest. The transition from smooth spaces to singular spaces where calculus is possible parallels the classical ...
openaire   +1 more source

Proximal Bundle Method for Contact Shape Optimization Problem

Advances in Electrical and Electronic Engineering, 2017
From the mathematical point of view, the contact shape optimization is a problem of nonlinear optimization with a specific structure, which can be exploited in its solution. In this paper, we show how to overcome the difficulties related to the nonsmooth
Nikola Plivova, Petr Beremlijski
doaj   +1 more source

Nonsmooth Calculus in Finite Dimensions

SIAM Journal on Control and Optimization, 1987
New calculus rules are given for the Clarke generalized gradient \(\partial f\) of a general lower semicontinuous function \(f: {\mathbb{R}}^ n\to {\mathbb{R}}\cup \{\pm \infty \}\). These include rules for computing \(\partial f\) when \(f=f_ 1+f_ 2\circ F\) in cases where \(f_ 1\), \(f_ 2\) are l.s.c. and F is either stricly differentiable or isotone.
Ward, D. E., Borwein, J. M.
openaire   +3 more sources

Restrictive metric regularity and generalized differential calculus in Banach spaces

International Journal of Mathematics and Mathematical Sciences, 2004
We consider nonlinear mappings f:X→Y between Banach spaces and study the notion of restrictive metric regularity of f around some point x¯, that is, metric regularity of f from X into the metric space E=f(X).
Boris S. Mordukhovich, Bingwu Wang
doaj   +1 more source

Nonsmooth Analysis: Differential Calculus of Nondifferentiable Mappings [PDF]

Transactions of the American Mathematical Society, 1981
A new approach to local analysis of nonsmooth mappings from one Banach space into another is suggested. The approach is essentially based on the use of set-valued mappings of a special kind, called fans, for local approximation. Convex sets of linear operators provide an example of fans.
openaire   +2 more sources

Global dissipativity and quasi-Mittag-Leffler synchronization of fractional-order complex-valued neural networks with time delays and discontinuous activations

Nonlinear Analysis
This paper explores fractional-order complex-valued neural networks (FOCVNNs) with time delays and discontinuous activation functions. A novel fractional-order inequality is utilized to study this system as a whole without dividing it into different ...
Libo Wang, Guigui Xu
doaj   +1 more source

Convex Subcones of the Contingent Cone in Nonsmooth Calculus and Optimization [PDF]

Transactions of the American Mathematical Society, 1987
The tangential approximants most useful in nonsmooth analysis and optimization are those which lie "between" the Clarke tangent cone and the Bouligand contigent cone. A study of this class of tangent cones is undertaken here. It is shown that although no convex subcone of the contingent cone has the isotonicity property of the contingent cone, there ...
openaire   +1 more source

Nonsmooth Problems of Calculus of VariationsviaCodifferentiation [PDF]

ESAIM: Control, Optimisation and Calculus of Variations, 2014
In this paper multidimensional nonsmooth, nonconvex problems of the calculus of variations with codifferentiable integrand are studied. Special classes of codifferentiable functions, that play an important role in the calculus of variations, are introduced and studied.
openaire   +1 more source

$H_\infty$-calculus for elliptic operators with nonsmooth coefficients

Differential and Integral Equations, 1997
The authors consider general systems of elliptic operators on \(R^n\) and on compact manifolds. They prove under minimal regularity assumptions on the coefficients that there exists a bounded holomorphic functional calculus in \(L_p\) spaces which was introduced by \textit{A. McIntosh} [Operator theory and partial differential equations, Proc.
Duong, Xuan T., Simonett, Gieri
openaire   +3 more sources