zbMATH — the first resource for mathematics

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.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
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)
Preinvex functions and weak efficient solutions for some vectorial optimization problem in Banach spaces. (English) Zbl 1095.90105
The authors generalize the definition of preinvexity to mappings taking values in a Banach space. They prove a Gordan type alternative theorem for such functions and use it to derive necessary optimality conditions for scalar optimization problems with preinvex objective and constraint functions. These conditions are then extended to vector optimization problems by means of a scalarization result for weakly efficient points of preinvex mappings. Sufficient optimality conditions for such preinvex vector optimization problems are also obtained. Finally, the authors prove that local weakly efficient points of preinvex mappings are necessarily global weakly efficient.

90C29Multi-objective programming; goal programming
26B25Convexity and generalizations (several real variables)
90C46Optimality conditions, duality
Full Text: DOI