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On the density of proper efficient points

Author: Fu Wantao
Journal: Proc. Amer. Math. Soc. 124 (1996), 1213-1217
MSC (1991): Primary 90C31
MathSciNet review: 1301051
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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 [Enhancements On Off] (What's this?)

  • 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

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Additional Information

Fu Wantao
Affiliation: Department of Mathematics, Nanchang University, Nanchang, Jiangxi, 330047, People’s Republic of China

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
Article copyright: © Copyright 1996 American Mathematical Society

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