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)
Some variants of the Ekeland variational principle for a set-valued map. (English) Zbl 1064.49018
Summary: This paper deals with the Ekeland variational principle (EVP) for a set-valued map F with values in a vector space E. Using the concept of cone extension and the Mordukhovich coderivative, we formulate some variants of the EVP for F under various continuity assumptions. We investigate also the stability of a set-valued EVP. Our approach is motivated by the set approach proposed by Kuroiwa for minimizing set-valued maps.

49J53Set-valued and variational analysis
49J52Nonsmooth analysis (other weak concepts of optimality)
[1] · Zbl 0286.49015 · doi:10.1016/0022-247X(74)90025-0
[2] · Zbl 0779.49015 · doi:10.1287/moor.18.1.173
[3] · Zbl 0936.49012 · doi:10.1007/s001860050020
[4] · Zbl 1042.90036 · doi:10.1023/A:1004663208905
[5] · Zbl 1053.49019 · doi:10.1006/jmaa.2000.7357
[6] · Zbl 1029.49020 · doi:10.1080/02331930211982
[7]Kuroiwa, D., Some Duality Theorems for Set-Valued Optimization with Natural Criteria, Proceedings of the International Conference on Nonlinear Analysis and Convex Analysis, World Scientific, Singapore, Republic of Singapore, pp. 221-228, 2001.
[8] · Zbl 1042.49524 · doi:10.1016/S0362-546X(01)00274-7
[9] · Zbl 0595.90085 · doi:10.1007/BF00940198
[12] · Zbl 0866.90103 · doi:10.1007/BF02192246
[13]Fan, K., A Minimax Inequality and Applications, Inequalities III, Proceeding of the 3rd Symposium Dedicated to the Memory of Theodore S. Motzkin, University of California, Los Angeles, California 1969; Academic Press, New York, NY, pp. 103-113, 1972.
[17] · Zbl 0881.49009 · doi:10.1090/S0002-9947-96-01543-7