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Scalarization in vector optimization. (English) Zbl 0539.90093

A scalarization of a general nonconvex vector optimization problem is investigated. Scalarization means the replacement of the vector optmization problem by a scalar optimization problem. Under suitable assumptions it is shown that an optimal solution of the considered vector optimization problem is also a solution of an appropriate approximation problem. With the aid of this theory a complete characterization of minimal and weakly minimal elements of a nonempty nonconvex subset of a partially ordered real linear space is presented. Moreover, these results are applied to general vector approximation problems.

MSC:

90C31 Sensitivity, stability, parametric optimization
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