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Contractibility of the efficient frontier of three-dimensional simply-shaded sets. (English) Zbl 1054.90065
Summary: 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 A. Danilidis, N. Hadjisavvas, and S. Schaible [J. Optimization Theory Appl. 93, No. 3, 517–524 (1997; Zbl 0879.90159)] regarding the connectedness of the efficient outcome set for three-criteria optimization problems involving continuous semistrictly quasiconcave objective functions.

MSC:
90C29 Multi-objective and goal programming
90C31 Sensitivity, stability, parametric optimization
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