Results 161 to 170 of about 810 (214)

Quantile Regression for Analyzing Heterogeneity in Ultra-high Dimension. [PDF]

J Am Stat Assoc, 2012
Wang L, Wu Y, Li R.
europepmc   +1 more source

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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On Second-Order Subdifferentials and Their Applications

SIAM Journal on Optimization, 2001
The authors study second-order subdifferentials of extended-real-valued functions. The starting point is the second-order subdifferential introduced by the first author as the coderivative of the first-order subdifferentiable mapping. Beside this, a semiconvex version is introduced as the coderivative of the convexified first-order subdifferential ...
Boris S Mordukhovich, Jiří V Outrata
exaly   +2 more sources

The properties of the weak subdifferentials

, 2010
This paper deals with the weak subdifferentials. The properties of the weak subdifferentials are examined. It is showed that the weak subdifferential of a function having a global minimum is not empty.
KASIMBEYLI, Refail, İNCEOĞLU, Gonca
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?-Subdifferentials in terms of subdifferentials

Set-Valued Analysis, 1996
In this note, we give a formula which expresses the e-subdifferential operator of a lower semicontinuous convex proper function on a given Banach space in terms of its subdifferential.
Juan-Enrique Martinez-Legaz, Michel Th�ra   +1 more
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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
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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
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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
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ON A PROPERTY OF THE SUBDIFFERENTIAL

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