Results 171 to 180 of about 2,908 (221)

Mean Value Property and Subdifferential Criteria for Lower Semicontinuous Functions

Transactions of the American Mathematical Society, 1995
International audienceWe define an abstract notion of subdifferential operator and an associated notion of smoothness of a norm covering all the standard situations.
Marc Lassonde, Didier Aussel
exaly   +2 more sources

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Hunting for a Smaller Convex Subdifferential

Journal of Global Optimization, 1997
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Vaithilingam Jeyakumar, V F Demyanov
exaly   +2 more sources

Lower Subdifferentiability and Integration

Set-Valued Analysis, 2002
This well written article is devoted to the question of integration of a multivalued operator \(T:X\to 2^{X^*}\), i.e., the problem of finding a function \(f\) such that, for a suitable notion of subdifferential, \(T\subset \partial f\). In this paper, the case where \(T\) is a \((L(x_0))\) multifunction with respect to some \(x_0\in \operatorname {Dom}
Bachir, Mohammed, Daniilidis, Aris, Penot, Jean-Paul   +2 more
openaire   +2 more sources

Subdifferentials with respect to dualities

ZOR Zeitschrift f�r Operations Research Methods and Models of Operations Research, 1995
Summary: Let \(X\) and \(W\) be two sets and \(\Delta: \overline R^X\to \overline R^W\) a duality (i.e., a mapping \(\Delta: f\in \overline R^X\to f^\Delta\in \overline R^W\) such that \((\inf_{i\in I} f_i)^\Delta= \sup_{i\in I} f^\Delta_i\) for all \(\{f_i\}_{i\in I}\subseteq \overline R^X\) and all index sets \(I\)).
Juan Enrique Martínez-Legaz, Ivan Singer   +1 more
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An Appropriate Subdifferential for Quasiconvex Functions

SIAM Journal on Optimization, 2002
In this paper we introduce and study a subdifferential that is related to the quasi- convex functions, much as the Fenchel--Moreau subdifferential is related to the convex ones. It is defined for any lower semicontinuous function, through an appropriate combination of an abstract subdifferential and the normal cone to sublevel sets.
Nicolas Hadjisavvas, Aris Daniilidis, Juan-Enrique Martínez-Legaz   +2 more
exaly   +3 more sources

Subdifferentiability and the Duality Gap

Positivity, 2002
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gretsky, N. E., Ostroy, J. M., Zame, W. R.   +2 more
openaire   +1 more source

ON A PROPERTY OF THE SUBDIFFERENTIAL

Mathematics of the USSR-Sbornik, 1993
See the review Zbl 0748.49003.
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Enlarged Inclusion of Subdifferentials

Canadian Mathematical Bulletin, 2005
Abstract This paper studies the integration of inclusion of subdifferentials. Under various verifiable conditions, we obtain that if two proper lower semicontinuous functions f and g have the subdifferential of f
Thibault, Lionel, Zagrodny, Dariusz
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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
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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, Michel H., Lassonde, Marc
openaire   +3 more sources