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.
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Communicated by G. Leitmann
The author is grateful to the reviewer for many valuable comments and helpful suggestions.
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Luc, D.T. On duality theory in multiobjective programming. J Optim Theory Appl 43, 557–582 (1984). https://doi.org/10.1007/BF00935006
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DOI: https://doi.org/10.1007/BF00935006