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)
Schemes for finding minimum-norm solutions of variational inequalities. (English) Zbl 1183.49012

Summary: Consider the Variational Inequality (VI) of finding a point x * such that

x * Fix(T)and(I-S)x * ,x-x * 0,xFix(T)(*)

where T,S are nonexpansive self-mappings of a closed convex subset C of a Hilbert space, and Fix(T) is the set of fixed points of T. Assume that the solution set Ω of this VI is nonempty. This paper introduces two schemes, one implicit and one explicit, that can be used to find the minimum-norm solution of VI (*); namely, the unique solution x * to the quadratic minimization problem: x * =argmin xΩ x 2 .

MSC:
49J40Variational methods including variational inequalities
47J20Inequalities involving nonlinear operators
47H09Mappings defined by “shrinking” properties
65J15Equations with nonlinear operators (numerical methods)