Convex analysis in general vector spaces

By Constantin Zalinescu. 2002

2,089 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

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Citations in the corpus

Smoothness, Low Noise and Fast Rates (2010, neutral): “In order to consider general norms, we will also need to rely on a non-negative regularizer F : W 7→ R that is a 1-strongly convex (see Deﬁnition in e.g. [33]) w.r.t. to the norm w for all w ∈ W .”
Regularization Techniques for Learning with Matrices (2009, background): “The above theorem can be found, for instance, in Zalinescu [2002] (see Corollary 3.5.11 on p. 217 and Remark 3.5.3 on p. 218).”
Proximity for sums of composite functions (2010, background): “Let us note that such splitting algorithms are already available to solve Problem 1.1 under certain restrictions.”
Higher moment coherent risk measures (2007, background): “By (C1), axioms (A1) and (A2) imply that (0)¼ 0, which allows one to rewrite (16) as ðXÞ ¼ sup 40 ð Xþ 0Þ ð0Þ ¼ 0þðXÞ, ð17Þ where the last equality in (17) comes from the definition of the recession function (Rockafellar 1970, Zălinescu 2002).”
Forward-Douglas–Rachford splitting and forward-partial inverse method for solving monotone inclusions (2012, background): “Let us first recall some standard notation and results.[37,38] We denote by 0(H) be the class of lower semicontinuous convex functions f : H → ]−∞,+∞] such that dom f = {x ∈ H | f (x) < +∞} = ∅.”
Convex Optimization in Normed Spaces: Theory, Methods and Examples (2015, background): “For a more general functional setting, see [10], [53] and [105].”
Fitzpatrick functions, cyclic monotonicity and Rockafellar's antiderivative (2007, neutral): “E-mail: bartz@techunix.technion.ac.il.”
Dual characterization of properties of risk measures on Orlicz hearts (2008, positive): “So Theorem 2.4.10 of Zălinescu (2002) yields that ρ is Gâteauxdifferentiable at X with ∇ρ(X) = −ξ. Remark 3.3.”
The Baillon-Haddad Theorem Revisited (2009, background): “For background on convex analysis, we refer the reader to [12, 17, 22].”