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Lagrangian function and duality theory in multiobjective programming with set functions. (English) Zbl 0619.90072
Using the concept of vector-valued Lagrangian functions, we characterize a special class of solutions, D-solutions, of a multiobjective programming problem with set functions in which the domination structure is described by a closed convex cone D. Properties of two perturbation functions, primal map and dual map, are also studied. Results lead to a general duality theorem.

MSC:
90C31 Sensitivity, stability, parametric optimization
49N15 Duality theory (optimization)
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