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)
Existence of solutions for vector optimization problems. (English) Zbl 0911.90290
Summary: We define the generalized efficient solution which is more general than the weakly efficient solution for vector optimization problems, and prove the existence of the generalized efficient solution for nondifferentiable vector optimization problems by using vector variational-like inequalities for set-valued maps. $\copyright$ Academic Press.

MSC:
90C29Multi-objective programming; goal programming
WorldCat.org
Full Text: DOI
References:
[1] Borwein, J. M.: On the existence of Pareto efficient points. Math. oper. Res. 8, 64-73 (1983) · Zbl 0508.90080
[2] Corley, H. W.: An existence result for maximization with respect to cones. J. optim. Theory appl. 31, 277-281 (1980) · Zbl 0416.90068
[3] Jahn, J.: Mathematical vector optimization in partially ordered linear spaces. (1986) · Zbl 0578.90048
[4] Yu, P. L.: Cone convexity, cone extreme points and nondominated solutions in decision problems with multi-objectives. J. optim. Theory appl. 14, 319-377 (1974) · Zbl 0268.90057
[5] Chen, G. Y.; Craven, B. D.: Existence and continuity of solutions for vector optimization. J. optim. Theory appl. 81, 459-468 (1994) · Zbl 0810.90112
[6] Fan, K.: A generalization of tychonoff’s fixed point theorem. Math. ann. 142, 305-310 (1961) · Zbl 0093.36701
[7] Kazmi, K. R.: Existence of solutions for vector optimization. Appl. math. Lett. 9, 19-22 (1996) · Zbl 0869.90063
[8] Giannessi, F.: Theorems of alternative, quadratic programs and complementarity problems. Variational inequalities and complementarity problems (1980) · Zbl 0484.90081
[9] Chen, G. Y.: Existence of solutions for a vector variational inequality: an extension of the hartman--stampacchia theorem. J. optim. Theory appl. 74, 445-456 (1992) · Zbl 0795.49010
[10] Chen, G. Y.; Li, S. J.: Existence of solutions for generalized vector quasi-variational inequality. J. optim. Theory appl. 90, 321-334 (1996) · Zbl 0869.49005
[11] Konnov, I. V.; Yao, J. C.: On the generalized vector variational inequality problem. J. math. Anal. appl. 206, 42-58 (1997) · Zbl 0878.49006
[12] Lee, B. S.; Lee, G. M.; Kim, D. S.: Generalized vector variational-like inequalities on locally convex Hausdorff topological vector spaces. Indian J. Pure appl. Math. 28, 33-41 (1997) · Zbl 0899.49005
[13] Lai, T. C.; Yao, J. C.: Existence results for VVIP. Appl. math. Lett. 9, 17-19 (1996) · Zbl 0886.49008
[14] Lee, G. M.; Kim, D. S.; Lee, B. S.; Cho, S. J.: Generalized vector variational inequality and fuzzy extension. Appl. math. Lett. 6, 47-51 (1993) · Zbl 0804.49004
[15] Lee, G. M.; Kim, D. S.; Lee, B. S.; Cho, S. J.: On vector variational inequality. Bull. korean math. Soc. 33, 553-564 (1996) · Zbl 0871.49011
[16] Lee, G. M.; Lee, B. S.; Chang, S. S.: On vector quasivariational inequalities. J. math. Anal. appl. 203, 626-638 (1996) · Zbl 0866.49016
[17] G. M. Lee, D. S. Kim, B. S. Lee, N. D. Yen, Vector variational inequality as a tool for studying vector optimization problems, Nonlinear Anal. · Zbl 0956.49007
[18] Lin, L. J.: Pre-vector variational inequalities. Bull. austral. Math. soc. 53, 63-70 (1996) · Zbl 0858.49008
[19] Lin, K. L.; Yang, D. P.; Yao, J. C.: Generalized vector variational inequalities. J. optim. Theory appl. 92, 117-125 (1997) · Zbl 0886.90157
[20] Siddiqi, A. H.; Ansari, A. H.; Khaliq, A.: On vector variational inequalities. J. optim. Theory appl. 84, 171-180 (1995) · Zbl 0827.47050
[21] Yang, X. Q.: Generalized convex functions and vector variational inequalities. J. optim. Theory appl. 79, 563-579 (1993) · Zbl 0797.90085
[22] Yu, S. J.; Yao, J. C.: On vector variational inequalities. J. optim. Theory appl. 89, 749-769 (1996) · Zbl 0848.49012
[23] Clarke, F. H.: Optimization and nonsmooth analysis. (1983) · Zbl 0582.49001
[24] Hanson, M. A.: On sufficiency of the Kuhn--Tucker conditions. J. math. Anal. appl. 80, 545-550 (1982) · Zbl 0463.90080
[25] Giorgi, G.; Guerraggio, A.: Various types of nonsmooth invex functions. J. inform. Optim. sci. 17, 137-150 (1996) · Zbl 0859.49020
[26] Sawaragi, Y.; Nakayama, H.; Tanino, T.: Theory of multiobjective optimization. (1985) · Zbl 0566.90053
[27] Yao, J. C.; Guo, J. S.: Variational and generalized variational inequalities with discontinuous mappings. J. math. Anal. appl. 182, 371-392 (1994) · Zbl 0809.49005
[28] Aubin, J. P.: Optima and equilibria. (1993)
[29] Chang, S. S.; Lee, B. S.; Wu, X.; Cho, Y. J.; Lee, G. M.: On the generalized quasi-variational inequality problems. J. math. Anal. appl. 203, 686-711 (1996) · Zbl 0867.49008