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)
On gap functions for vector variational inequalities. (English) Zbl 0997.49006
Giannessi, Franco (ed.), Vector variational inequalities and vector equilibria. Mathematical theories. Dordrecht: Kluwer Academic Publishers. Nonconvex Optim. Appl. 38, 55-72 (2000).
Summary: We extend the theory of gap functions for scalar variational inequality problems [see {\it A. Auslender}: “Optimisation. Méthodes numériques” (1976; Zbl 0326.90057) and {\it F. Giannessi}, Ann. Oper. Res. 58, 181-200 (1995; Zbl 0844.90069)] to the case of vector variational inequalities. The gap functions for vector variational inequalities are defined as set-valued mappings. The significance of the gap function is interpreted in terms of the inverse vector variational inequality. Convexity properties of these set-valued mappings are studied under different assumptions. For the entire collection see [Zbl 0952.00009].

49J40Variational methods including variational inequalities
90C33Complementarity and equilibrium problems; variational inequalities (finite dimensions)