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)
New optimality conditions and duality results of G type in differentiable mathematical programming. (English) Zbl 1143.90034
Summary: A new class of differentiable functions, called G-invex functions with respect to η , is introduced by extending the definition of invex functions. New necessary optimality conditions of G-F. John and G-Karush-Kuhn-Tucker type are obtained for differentiable constrained mathematical programming problems. The G-invexity concept introduced is used to prove the sufficiency of these necessary optimality conditions. Further, a so-called G-Mond-Weir-type dual is formulated and various duality results are also established by assuming the functions involved to be G-invex with respect to the same function η .
MSC:
90C46Optimality conditions, duality
90C26Nonconvex programming, global optimization
26B25Convexity and generalizations (several real variables)