Results 171 to 180 of about 2,024 (222)

Subdifferential calculus for a quasiconvex function with generator

Journal of Mathematical Analysis and Applications, 2011
Recently, we discussed optimality conditions for quasiconvex programming by introducing ‘Q-subdifferential’, which is a notion of differential of quasiconvex functions.
Daishi Kuroiwa
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$$\varepsilon $$ ε -Subdifferential as an Enlargement of the Subdifferential

Bulletin of the Iranian Mathematical Society, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Rezaie, Mahboubeh, Mirsaney, Zahra Sadat
openaire   +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   +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
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
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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
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
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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, M., Lassonde, M.
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Subdifferentiation of Regularized Functions

Set-Valued and Variational Analysis, 2016
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Huynh, van Ngai, Penot, Jean-Paul
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