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)
Generalized vector variational inequality and its duality for set-valued maps. (English) Zbl 0940.49008
Summary: We consider a Generalized Vector Variational Inequality (GVVI) for set-valued maps, give its dual form DVVI, and prove an equivalence between GVVI and DVVI.

MSC:
49J40Variational methods including variational inequalities
49J53Set-valued and variational analysis
WorldCat.org
Full Text: DOI
References:
[1] Giannessi, F.: Theorems of alternative, quadratic programs and complementarity problems. Variational inequalities and complementarity problems, 151-186 (1980) · Zbl 0484.90081
[2] Chen, G. Y.; Cheng, G. M.: Vector variational inequality and vector optimizations. Lecture notes in economics and mathematical systems 285, 408-416 (1987)
[3] Chen, G. Y.; Craven, B. D.: Approximate dual and approximate vector variational inequality for multiobjective optimization. J. austral. Math. soc. (Series A) 47, 418-423 (1989) · Zbl 0693.90089
[4] Chen, G. Y.; Craven, B. D.: A vector variational inequality and optimization over an efficient set. Zor-meth. Models op. Res. 34, 1-12 (1990) · Zbl 0693.90091
[5] Chen, G. Y.; Yang, X. Q.: The vector complementarity problem and its equivalence with the weak minimal element in ordered sets. J. math. Anal. appl. 153, 136-158 (1990) · Zbl 0712.90083
[6] Chen, G. Y.: Existence of solutions for a vector variational inequality: an extension of hartman-stampacchia theorem. J. optim. Th. appl. 74, No. 3, 445-456 (1992) · Zbl 0795.49010
[7] Chen, G. Y.; Li, S. J.: Existence of solutions for a generalized vector quasivariational inequality. J. optim. Th. appl. 90, No. 2, 321-334 (1996) · Zbl 0869.49005
[8] Lee, G. M.; Kim, D. S.; Lee, B. S.; Cho, S. J.: Generalized vector variational inequality and fuzzy extension. Appl. math. Lett. 6, No. 6, 47-51 (1993) · Zbl 0804.49004
[9] Lee, G. M.; Lee, B. S.; Chang, S. -S.: On vector quasivariational inequalities. J. math. Anal. appl. 203, 626-638 (1966) · Zbl 0866.49016
[10] Lee, G. M.; Kim, D. S.; Lee, B. S.: Generalized vector variational inequality. Appl. math. Lett. 9, No. 1, 39-42 (1996) · Zbl 0862.49014
[11] Siddiqi, A. H.; Ansari, Q. H.; Khaliq, A.: On vector variational inequalities. J. optim. Th. appl. 84, 171-180 (1995) · Zbl 0827.47050
[12] Yang, X. Q.: Generalized convex functions and vector variational inequalities. J. optim. Th. appl. 79, 563-580 (1993) · Zbl 0797.90085
[13] Yang, X. Q.: Vector variational inequality and its duality. Nonlinear analysis, T.M.A. 21, 869-877 (1993) · Zbl 0809.49009
[14] Yu, S. J.; Yao, J. C.: On vector variational inequalities. J. optim. Th. appl. 89, 749-769 (1996) · Zbl 0848.49012
[15] Fan, K.: A generalization of tychonoff’s fixed point theorem. Math. ann. 142, 305-310 (1961) · Zbl 0093.36701
[16] Sawaragi, Y.; Nakayama, H.; Tanino, T.: Theory of multiobjective optimization. (1985) · Zbl 0566.90053
[17] Yang, X. Q.: A Hahn-Banach theorem in ordered linear space and its applications. Optimization 25, 1-9 (1992) · Zbl 0834.46006
[18] Mosco, U.: Dual variational inequalities. J. math. Anal. appl. 40, 202-206 (1972) · Zbl 0262.49003
[19] Jameson, G.: Ordered linear spaces. Lecture notes in mathematics 141 (1970) · Zbl 0196.13401