Results 171 to 180 of about 810 (214)

Stability of Slopes and Subdifferentials

Set-Valued Analysis, 2003
Given a Banach space \(X\) and a function \(f:X\rightarrow\mathbb{R\cup \{+\infty\}}\), its slope is the function defined by \(\text{slope} f(x)=\lim\sup_{y\rightarrow x,y\neq x}\frac{(f(x)-f(y))^{+}}{\left\| x-y\right\| }\) where \(\alpha^{+}=\max\{0,\alpha\}\) for \(x\in \text{dom}f\), while \(\text{slope}f(x)=+\infty\) for \(x\notin\text{dom}f\). In
Geoffroy, M., Lassonde, M.
openaire   +3 more sources

Subdifferentiation of Regularized Functions

Set-Valued and Variational Analysis, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Huynh, van Ngai, Penot, Jean-Paul
openaire   +2 more sources

On the subdifferential of a submodular function

Mathematical Programming, 1984
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +2 more sources

Hunting for a Smaller Convex Subdifferential

Journal of Global Optimization, 1997
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Vladimir F. Demyanov, Vaithilingam Jeyakumar   +1 more
openaire   +1 more source

An Appropriate Subdifferential for Quasiconvex Functions

SIAM Journal on Optimization, 2002
The authors introduce a concept of subdifferential that is well adapted to the class of lower-semicontinuous quasiconvex functions. Several interesting properties and calculus rules are established. A related reference is [\textit{J. E. Martínez-Legaz} and \textit{J. E. Sach}, J. Convex Anal. 6, 1-11 (1999; Zbl 0942.49020)].
Aris Daniilidis, Nicolas Hadjisavvas, Juan Enrique Martínez-Legaz   +2 more
openaire   +2 more sources

On the Subdifferentiability of Convex Operators

Journal of the London Mathematical Society, 1986
Let Y be an ordered vector space. Every convex operator ranging in Y admits directional minorant at each point and in every direction of its domain space if and only if every decreasing lower bounded sequence in Y possesses an infimum. This result, combined with a theorem of M. M.
openaire   +2 more sources

The Mordukhovich Subdifferentials and Directions of Descent

Journal of Optimization Theory and Applications, 2015
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Pham Duy Khanh, Jen-Chih Yao, Nguyen Dong Yen   +2 more
openaire   +2 more sources

Weak Convexity and Approximate Subdifferentials

Journal of Optimization Theory and Applications
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wim van Ackooij, Felipe Atenas, Claudia A. Sagastizábal   +2 more
openaire   +2 more sources

Approximations of Subdifferentials

2014
In practice, the computation of subdifferential is not an easy task. In this chapter, we first consider some families of set-valued mappings that can be used to approximate subdifferentials. Then we define the concept of a discrete gradient that can be used as an approximation of the subgradient at a given point.
Adil Bagirov, Napsu Karmitsa, Marko M. Mäkelä   +2 more
openaire   +1 more source

On σ-Subdifferential Polarity and Fréchet σ-Subdifferential

Numerical Functional Analysis and Optimization, 2023
Mohammad Hossein Alizadeh, Javad Hosseinabadi   +1 more
openaire   +1 more source