Contractibility of the Efficient Frontier of Three-Dimensional Simply-Shaded Sets

J. Benoist and N. Popovici
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J. Benoist: University of Limoges
N. Popovici: Babes-Bolyai University

Journal of Optimization Theory and Applications, 2001, vol. 111, issue 1, No 5, 116 pages

Abstract: Abstract The aim of this paper is to study the geometrical and topological structure of the efficient frontier of simply-shaded sets in a three-dimensional Euclidean space with respect to the usual positive cone. Our main result concerns the contractibility of the efficient frontier and refines a recent result of Daniilidis, Hadjisavvas, and Schaible (Ref. 1) regarding the connectedness of the efficient outcome set for three-criteria optimization problems involving continuous semistrictly quasiconcave objective functions.

Keywords: Vector optimization; efficiency; contractibility; semistrict quasiconcavity (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1023/A:1017571214523

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