Abstract
This paper offers first- and higher-order necessary conditions for the local disjointness of a finite system of sets that are nonlinear inverse images of convex sets. The proof is based on the characterizations of α-admissible and α-tangent variations to nonlinear inverse images of convex sets and a necessary condition for the local disjointness in terms of these variations. As an application, the results are used to obtain first- and higher-order necessary conditions of optimality in constrained optimization problems.
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This research was supported by the Hungarian Research Fund (OTKA) Grant Nos. K-62316, NK-68040.
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Baják, S., Páles, Z. A separation theorem for nonlinear inverse images of convex sets. Acta Math Hung 124, 125–144 (2009). https://doi.org/10.1007/s10474-009-8164-4
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DOI: https://doi.org/10.1007/s10474-009-8164-4
Key words and phrases
- Hahn-Banach separation theorem
- Dubovitskii-Milyutin separation theorem
- inverse images of convex sets
- admissible variation
- tangent variation