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ON THE GRENANDER ESTIMATOR AT ZERO. [PDF]
Stat Sin, 2011 Balabdaoui F +4 more
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Beyond Low Rank + Sparse: Multi-scale Low Rank Matrix Decomposition. [PDF]
IEEE J Sel Top Signal Process, 2016 Ong F, Lustig M.
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Quantile Regression for Analyzing Heterogeneity in Ultra-high Dimension. [PDF]
J Am Stat Assoc, 2012 Wang L, Wu Y, Li R.
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?-Subdifferentials in terms of subdifferentials
Set-Valued Analysis, 1996In 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 +1 more
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$$\varepsilon $$ ε -Subdifferential as an Enlargement of the Subdifferential
Bulletin of the Iranian Mathematical Society, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Rezaie, Mahboubeh, Mirsaney, Zahra Sadat
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$\alpha $-Lower Subdifferentiable Functions
SIAM Journal on Optimization, 1993Let \(X\) be a locally convex real topological vector space, with dual \(X^*\), \(K\) a convex subset of \(X\) and \(\alpha\in (0,1]\). A function \(f: K\to \overline {\mathbb{R}}\) is said to be \(\alpha\)-lower subdifferentiable \((\alpha\)-l.s.d.) at \(x_ 0\in K\) if \(f(x_ 0)\in\mathbb{R}\) and there exists \(\omega\in X^*\) such that \(f(x)\geq f ...
Martínez-Legaz, J. E. +1 more
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Generalized weak subdifferentials
Optimization, 2011In this article, generalized weak subgradient (gw-subgradient) and generalized weak subdifferential (gw-subdifferential) are defined for nonconvex functions with values in an ordered vector space. Convexity and closedness of the gw-subdifferential are stated and proved.
İlknur Atasever Güvenç
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Lower Subdifferentiability and Integration
Set-Valued Analysis, 2002This 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 +2 more
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Enlarged Inclusion of Subdifferentials
Canadian Mathematical Bulletin, 2005AbstractThis 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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Subdifferentiation of Regularized Functions
Set-Valued and Variational Analysis, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Huynh, van Ngai, Penot, Jean-Paul
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