Cybernetics and Systems Analysis

, Volume 47, Issue 1, pp 95–105 | Cite as

Categorical properties of solvability for one class of minimization problems1

  • V. V. Semenov


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.


density Baire category solvability minimization semicontinuity Kadets–Klee property vector optimization 


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Copyright information

© Springer Science+Business Media, Inc. 2011

Authors and Affiliations

  1. 1.Taras Shevchenko National University of KyivKyivUkraine

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