On duality theory in multiobjective programming
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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.
Key WordsLagrangian functions M-convexity saddle points Slater's constraint qualification dual functions conjugate functions
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