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)
On the convexification procedure for nonconvex and nonsmooth infinite dimensional optimization problems. (English) Zbl 0755.49013
The paper gives a generalization and modification of a convexification procedure of D. P. Bertsekas [J. Optimization Theory Appl. 29, 169- 197 (1979; Zbl 0389.90080)] for infinite dimensional, nonsmooth and nonconvex optimization problems. A nonconvex minimization problem is being transformed into a convex parametrical minimization problem and an additional minimization of an everywhere Fréchet differentiable nonconvex function. The convexification of the nonconvex cost function f to ensue by means of a strongly convex function g, so that f+g is also a strongly convex function. One can prove a connection with the duality theory of J. F. Toland [J. Math. Anal. Appl. 66, 399-415 (1978; Zbl 0403.90066)] and give a descent method for the original problem.
Reviewer: H.Dietrich
MSC:
49N15Duality theory (optimization)
90C48Programming in abstract spaces
49M05Numerical methods in calculus of variations based on necessary conditions
90C26Nonconvex programming, global optimization