Results 121 to 130 of about 335 (149)

The Apparatus of Subdifferential Calculus

1995
The present chapter is the culmination of the book. Here, grounding on the alreadydeveloped methods, we deduce the main formulas of subdifferential calculus.
A. G. Kusraev, S. S. Kutateladze
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Metric regularity and subdifferential calculus

Russian Mathematical Surveys, 2000
Let \(X\) and \(Y\) be complete metric spaces. The closed-set-valued mapping \(F: X\Rightarrow Y\) is called \textit{metrically regular} on the set \(V\subset X\times Y\) if there exists a number \(K>0\) such that \[ d(x, F^{-1}(y))\leq K\cdot d(y, F(x))\quad \forall(x,y)\in V. \] This notion is closely connected with important principles of smooth and
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Lower semicontinuous type regularity conditions for subdifferential calculus

Optimization Methods and Software, 2010
We give a lower semicontinuous type regularity condition and a closedness type one which turn out to be necessary and sufficient for the fulfilment of two different formulae involving the e-subdifferential of a perturbation function, respectively.
Radu Ioan Bot, Sorin-Mihai Grad
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Lower semicontinuous Lyapunov functions and subdifferential calculus

Proceedings of the 41st IEEE Conference on Decision and Control, 2002., 2003
We show that lower semicontinuous Lyapunov functions can be used to determine both stable and attractive sets of differential equations with a short proof similar to that of the original Lyapunov indirect method. Several examples illustrate the flexibility of using such lower semicontinuous Lyapunov functions.
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Convex Analysis and Subdifferential Calculus

2015
This chapter deals with several properties of convex functions, especially in connection with their regularity, on the one hand, and the characterization of their minimizers, on the other. We shall explore sufficient conditions for a convex function to be continuous, as well as several connections between convexity and differentiability.
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Subdifferential calculus in abstract convex cones

2017 Constructive Nonsmooth Analysis and Related Topics (dedicated to the memory of V.F. Demyanov) (CNSA), 2017
In this paper a new special class of separable normed cones is selected by us. This class includes cones in normed spaces as well as cones in linear spaces with asymmetric norms. Examples of separable normed cones that do not admit a linear injective isometric embedding in a normed space are given.
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First-Order Subdifferential Calculus

2018
This chapter concerns generalized differential properties of extended-real-valued functions \(\varphi: \mathbb{R}^{n} \rightarrow \overline{\mathbb{R}}\) that are assumed, unless otherwise stated, to be lower semicontinuous around references points.
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Calculus of directional subdifferentials and coderivatives in Banach spaces

Positivity, 2016
The authors provide a quite complete study on directional versions of Mordukhovich nonsmooth constructions in general Banach spaces. More precisely, the objects of investigations are normal cones to nonsmooth sets, coderivatives of set-valued mappings, and subdifferentials of extended-real-valued functions, for which characterizations, basic properties
Long, Pujun, Wang, Bingwu, Yang, Xinmin
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Subdifferential Calculus

2023
Piernicola Bettiol, Richard Vinter
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Other subdifferential calculus rules

2023
Rafael Correa, Abderrahim Hantoute, Marco A. López   +2 more
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