Results 1 to 10 of about 425 (153)

Constrained nonsmooth problems of the calculus of variations [PDF]

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 ...
Maksim Dolgopolik
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Generalized Differential Calculus for Nonsmooth and Set-Valued Mappings

Journal of Mathematical Analysis and Applications, 1994
Some generalized differentiability concepts for multifunctions and nonsmooth mappings in \(\mathbb{R}^ n\) are studied. In this paper the most important one is the so-called coderivative of multifunctions introduced earlier [the author, Dokl. Akad. Nauk SSSR 254, 1072-1076 (1980; Zbl 0491.49011)] using the normal cone to the graph in the sense given by
B S Mordukhovich
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Asymptotic stationarity and regularity for nonsmooth optimization problems [PDF]

Journal of Nonsmooth Analysis and Optimization, 2020
Based on the tools of limiting variational analysis, we derive a sequential necessary optimality condition for nonsmooth mathematical programs which holds without any additional assumptions. In order to ensure that stationary points in this new sense are
Patrick Mehlitz
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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 ...
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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.
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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
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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
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Preface to the Special Issue “Advanced Theories and Novel Methods for Nonlinear Analysis, Optimization and Applications”

Mathematics
After more than a century of unremitting efforts by scholars, nonlinear analysis has found widespread and important applications in many fields that are at the core of many branches of pure and applied mathematics, including functional analysis, fixed ...
Wei-Shih Du, Yousuke Araya
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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
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On solutions of Hamilton-Jacobi equations with exponential dependence on momentum

Современная математика: Фундаментальные направления
Three initial problems for one-dimensional Hamilton-Jacobi equations of evolutionary type are considered on a bounded time segment. In all problems, the Hamiltonians depend on the coordinate and momentum variables.
L. G. Shagalova
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