On a generalized best approximation problem
Journal of Approximation Theory
Linear variational principle for convex vector maximization
Cybernetics and Systems Analysis
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A lower semicontinuous functional disturbed by a Minkowski functional of a closed bounded convex neighborhood of zero possessing the Kadets---Klee property is minimized on a closed subset X of a reflexive Banach space E. It is proved that the set of parameters for which the problem has a solution contains a G驴-subset dense in E \ X. It is shown that the reflexivity condition and the condition of the Kadets---Klee property of the neighborhood cannot be weakened. The application to optimization problems for linear systems with vector performance criteria is considered.