Efficient sets of convex compacta are arcwise connected

We prove that the efficient point set Max(Q|K) of a compact convex set Q⊂X in a Hausdorff topological vector space X ordered by a closed convex pointed cone K⊂X with nonempty K+i:={l⊂K\{0}:l(x)>0} is arcwise connected.

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Bibliographic Details
Published in:Journal of optimization theory and applications 2001-07, Vol.110 (1), p.159-172
Main Authors: MAKAROV, E. K, RACHKOVSKI, N. N
Format: Article
Language:English
Subjects:
Applied sciences
Exact sciences and technology
Mathematical programming
Operational research and scientific management
Operational research. Management science
Optimization
Vector space
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Summary:We prove that the efficient point set Max(Q|K) of a compact convex set Q⊂X in a Hausdorff topological vector space X ordered by a closed convex pointed cone K⊂X with nonempty K+i:={l⊂K\{0}:l(x)>0} is arcwise connected.
ISSN:0022-3239
1573-2878
DOI:10.1023/A:1017599614183