Properties of Uniform Tangent Sets and Lagrange Multiplier Rule

Abstract

The concept of uniform tangent sets was introduced and discussed in [3]. This study is devoted to their further investigation and to generalization of the abstract Lagrange multiplier rule from [3].

On tangential transversality

“…Since uniform tangent sets are closely connected to the Clarke subdiffrential (cf. [19] and [3]), the main results concern the Clarke tangent and normal cones. To be more precise, strong tangential transversality implies an intersection property for the Clarke tangent and normal cones and a rather general sum rule for the Clarke subdifferential.…”