A characterization of weakly efficient points. (English) Zbl 0834.90109
Summary: We study a characterization of weakly efficient solutions of multiobjective optimization problems (MOPs). We find that, under some quasiconvex conditions of the objective functions in a convex set of constraints, weakly efficient solutions of a MOP can be characterized as an optimal solution to a scalar constraint problem, in which one of the objectives is optimized and the remaining objectives are set up as constraints. This characterization is much less restrictive than those found in the literature up to now.
MSC:
| 90C29 | Multi-objective and goal programming |
| 26B25 | Convexity of real functions of several variables, generalizations |
References:
| [1] | H.P. Benson, ”Finding certain weakly efficient vertices in multiple objective linear fractional programming,”Management Science 31 (2) (1985). · Zbl 0619.90074 |
| [2] | V. Chankong and Y. Haimes,Multiobjective Decision Making: Theory and Methodology (North-Holland, Amsterdam, 1983). · Zbl 0622.90002 |
| [3] | J. Ecker and I. Kouada, ”Finding all efficient extreme points for multiple objective linear programs,”Mathematical Programming 14 (1978). · Zbl 0385.90105 |
| [4] | A. Geoffrion, ”Proper efficiency and theory of vector maximization,”Journal of Mathematical Analysis and Applications 22 (1968). · Zbl 0181.22806 |
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