Some Geometrical Aspects of Efficient Points in Vector Optimization |
| |
Authors: | X. Y. Zheng X. M. Yang K. L. Teo |
| |
Affiliation: | (1) Department of Mathematics, Yunnan University, Kunming, China;(2) Department of Mathematics, Chongqing Normal University, Chongqing, China;(3) Department of Mathematics and Statistics, Curtin University of Technology, Perth, Western Australia, Australia |
| |
Abstract: | We study efficient point sets in terms of extreme points, positive support points and strongly positive exposed points. In the case when the ordering cone has a bounded base, we prove that the efficient point set of a weakly compact convex set is contained in the closed convex hull of its strongly positive exposed points, thereby extending the Phelps theorem. We study also the density of positive proper efficient point sets. This research was supported by a Central Research Grant of Hong Kong Polytechnic University, Grant G-T 507. Research of the first author was also supported by the National Natural Science Foundation of P.R. China, Grant 10361008, and the Natural Science Foundation of Yunnan Province, China, Grant 2003A002M. Research of the second author was also supported by the Natural Science Foundation of Chongqing. Research of the third author was supported by a research grant from Australian Research Counsil. |
| |
Keywords: | Efficient points Extreme points Support points Strongly exposed points Normed spaces |
本文献已被 SpringerLink 等数据库收录! |
|