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)
A note on the multiple-set split convex feasibility problem in Hilbert space. (English) Zbl 1171.90009

The authors provide a gradient method for the (constrained) multiple-set split convex feasibility problem, finding a point

x i=1 p C i withT j xQ j ,j{1,,r}·

Here, C i H 1 and Q j H 2 are closed convex subsets of the Hilbert spaces H 1 and H 2 , respectively, and T j :H 1 H 2 are bounded linear operators. The method bases on the minimization of the function

f(x)=1 2 i=1 p α i |x-P C i (x)| 2 +1 2 j=1 r β j |T j x-P Q j (T j x)| 2

with suitable positive parameters α i and β j (where P denotes the projection operator).

It is shown that the iteration sequence generated by the method converges weakly to a solution of the problem. Assuming additional properties for the sets C i and Q j , even strong convergence can be proved.

MSC:
90C25Convex programming
49M37Methods of nonlinear programming type in calculus of variations
47H09Mappings defined by “shrinking” properties
47N10Applications of operator theory in optimization, convex analysis, programming, economics