Results 131 to 140 of about 508 (181)

$$\varepsilon $$ ε -Subdifferential as an Enlargement of the Subdifferential

Bulletin of the Iranian Mathematical Society, 2018
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Rezaie, Mahboubeh, Mirsaney, Zahra Sadat
exaly   +3 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   +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)].
N Hadjisavvas, Aris Daniilidis, Juan-Enrique Martínez-Legaz   +2 more
exaly   +3 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
openaire   +2 more sources

Subdifferentiability and the Duality Gap

Positivity, 2002
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Gretsky, N. E., Ostroy, J. M., Zame, W. R.   +2 more
openaire   +1 more source

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

ON A PROPERTY OF THE SUBDIFFERENTIAL

Mathematics of the USSR-Sbornik, 1993
See the review Zbl 0748.49003.
openaire   +2 more sources

Enlarged Inclusion of Subdifferentials

Canadian Mathematical Bulletin, 2005
AbstractThis 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 included in the γ-enlargement of the subdifferential of g, then the difference of those functions is γ-Lipschitz over their effective domain.
Thibault, Lionel, Zagrodny, Dariusz
openaire   +2 more sources

Subdifferentiation of Regularized Functions

Set-Valued and Variational Analysis, 2016
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Huynh, van Ngai, Penot, Jean-Paul
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On the subdifferential of a submodular function

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