zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
More than first-order developments of convex functions: primal-dual relations. (English) Zbl 0868.49014
Summary: The subject of this paper concerns the remainder term in the first-order development of a (finite-valued) convex function. We study functions for which this term is comparable to a squared norm and we relate it to the corresponding remainder term of the conjugate function. We show that a convex function satisfies a quadratic growth condition if and only if its subdifferential satisfies a linear growth condition. Finally, we define a new concept of “tangential regularization”, involving a local decomposition of N , along the subspace where the function is “smooth” and the subspace parallel to the subdifferential.
MSC:
49J52Nonsmooth analysis (other weak concepts of optimality)
26B25Convexity and generalizations (several real variables)
52A41Convex functions and convex programs (convex geometry)