|
On the density of proper efficient points
Author(s):
Fu
Wantao
Journal:
Proc. Amer. Math. Soc.
124
(1996),
1213-1217.
MSC (1991):
Primary 90C31
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
In this paper, our aim is to discuss the density of proper efficient points. As an interesting application of the results in this paper, we want to prove a density theorem of Arrow, Barankin, and Blackwell.
References:
- 1.
- D. T. Luc, Theory of vector optimization, Lecture Notes in Econom. and Math. Systems, vol. 319, Springer-Verlag, Berlin, 1989.
- 2.
- ------, Recession cones and the domination property in vector optimization, Math. Programming 49 (1990).
- 3.
- K. J. Arrow, E. W. Barankin, and D. Blackwell, Admissible points of convex sets, Contributions to the Theory of Games, Vol. II (H. W. Kuhn and A. W. Tucker, eds.), Princeton Univ. Press, Princeton, NJ, 1953. MR 14:998h
- 4.
- J. M. Borwein, The geometry of Parete efficiency over cones, Math. Operations forsch. Statist. 11 (1980). MR 83f:90110
- 5.
- J. Jahn, A generalization of a theorem of Arrow, Barankin, and Blackwell, SIAM J. Control Optim. 26 (1988). MR 89h:90224
- 6.
- W.-T. Fu, A note on the Arrow-Barankin-Blackwell theorem, J. Systems Sci. Math. Sci. (1994).
- 7.
- J. Jahn, Mathematical vector optimization in partially ordered linear spaces, Peter Lang, Frankfurt am Main, 1986. MR 87f:90095
- 8.
- G. R. Bitran and T. L. Magnanti, The structure of admissible points with respect to cone dominance, J. Optim. Theory Appl. 29 (1979), 573--614. MR 81e:90077
- 9.
- R. Hartley, On cone-efficiency, cone-convexity, and cone-compactness, SIAM J. Appl. Math. 34 (1978), 211--222. MR 58:7556
- 10.
- S. Helbig, Approximation of the efficient point set by perturbation of the ordering cone, Z. Oper. Res. 35 (1991), 197--220. MR 92g:90138
- 11.
- M. Petschke, On a theorem of Arrow, Barankin, and Blackwell, SIAM J. Control Optim. 28 (1990), 395--401. MR 91e:90096
- 12.
- W. Salz, Eine topologische Eigenschaft der effizienten Punkte konvexer Mengen, Oper. Res. Verfahren 23 (1976), 197--202. MR 80b:90124
- 13.
- A. Sterna-Karwat, Approximation families of cones and proper efficiency in vector optimization, Optimization 20 (1989), 809--817. MR 91j:90067
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(1991):
90C31
Retrieve articles in all Journals with MSC
(1991):
90C31
Additional Information:
Fu
Wantao
Affiliation:
Department of Mathematics, Nanchang University, Nanchang, Jiangxi, 330047, People's Republic of China
DOI:
10.1090/S0002-9939-96-03162-0
PII:
S 0002-9939(96)03162-0
Keywords:
Efficient point,
proper efficient point,
base of a cone,
density
Received by editor(s):
December 14, 1993
Received by editor(s) in revised form:
October 3, 1994
Communicated by:
Joseph S. B. Mitchell
Copyright of article:
Copyright
1996,
American Mathematical Society
|
Comments: webmaster@ams.org