On duality theory in multiobjective programming |
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Authors: | D. T. Luc |
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Affiliation: | (1) Computer and Automation Institute, Hungarian Academy of Sciences, Budapest, Hungary |
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Abstract: | In this paper, we study different vector-valued Lagrangian functions and we develop a duality theory based upon these functions for nonlinear multiobjective programming problems. The saddle-point theorem and the duality theorem are derived for these problems under appropriate convexity assumptions. We also give some relationships between multiobjective optimizations and scalarized problems. A duality theory obtained by using the concept of vector-valued conjugate functions is discussed.The author is grateful to the reviewer for many valuable comments and helpful suggestions. |
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Keywords: | Lagrangian functions M-convexity saddle points Slater's constraint qualification dual functions conjugate functions |
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