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Geometric consideration of duality in vector optimization. (English) Zbl 0534.90079
Recently, duality in vector optimization has been attracting the interest of many researchers. In order to derive duality in vector optimization, it seems natural to introduce some vector-valued Lagrangian functions with matrix (or linear operator, in some cases) multipliers. This paper gives an insight into the geometry of vector-valued Lagrangian functions and duality in vector optimization. It is observed that supporting cones for convex sets play a key role, as well as supporting hyperplanes, traditionally used in single-objective optimization.

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