Abstract
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 Gδ-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.
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1The study was financially supported by the State Fund for Basic Research of Ukraine, Grant No. 0108U010308.
Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 104–115, January–February 2011.
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Semenov, V.V. Categorical properties of solvability for one class of minimization problems1 . Cybern Syst Anal 47, 95–105 (2011). https://doi.org/10.1007/s10559-011-9293-7
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DOI: https://doi.org/10.1007/s10559-011-9293-7