Duality theory in multiobjective programming |
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Authors: | T. Tanino Y. Sawaragi |
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Affiliation: | (1) Department of Applied Mathematics and Physics, Faculty of Engineering, Kyoto University, Kyoto, Japan |
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Abstract: | In this paper, a multiobjective programming problem is considered as that of finding the set of all nondominated solutions with respect to the given domination cone. Two point-to-set maps, the primal map and the dual map, and the vector-valued Lagrangian function are defined, corresponding to the case of a scalar optimization problem. The Lagrange multiplier theorem, the saddle-point theorem, and the duality theorem are derived by using the properties of these maps under adequate convexity assumptions and regularity conditions. |
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Keywords: | Domination structures cone extreme points primal map vector-valued Lagrangian function dual map |
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