Some Geometrical Aspects of Efficient Points in Vector Optimization

X. Y. Zheng (), X. M. Yang and K. L. Teo
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X. Y. Zheng: Yunnan University
X. M. Yang: Chongqing Normal University
K. L. Teo: Curtin University of Technology

Journal of Optimization Theory and Applications, 2007, vol. 133, issue 2, No 10, 275-288

Abstract: 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.

Keywords: Efficient points; Extreme points; Support points; Strongly exposed points; Normed spaces (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1007/s10957-007-9171-7

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