Journal of Convex Analysis 32 (2025), No. 3, 767--788
Copyright Heldermann Verlag 2025
Transversality and Strong Tangential Transversality of a Finite Number of Sets
Nadezhda K. Ribarska
(1) Faculty of Mathematics and Informatics, Sofia University, Sofia, Bulgaria
(2) Inst. of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria
ribarska@fmi.uni-sofia.bg
Mariya Tasheva
Faculty of Mathematics and Informatics, Sofia University, Sofia, Bulgaria
mttasheva@uni-sofia.bg
A definition of strong tangential transversality for a finite number of sets is proposed such that strong tangential transversality implies transversality. The main tool in the proofs are infinitesimal characterizations of transversality and subtransversality of a finite number of sets in the prime space which are of independent interest. A normal intersection property for Clarke normal cones, a sum rule for the Clarke subdifferential of a finite number of lower semicontinuous functions, and an abstract Lagrange multiplier rule are obtained as applications.
Keywords: Sub(transversality), primal space characterizations, strong tangential transversality, normal intersection properties, sum rule, Lagrange multiplier rule.
MSC: 49K27, 49J53, 46N10.
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