On the nonsmooth regularity condition LIKQ for different abs-normal representations
Gannа Shyshkanova, Timo Kreimeier, Lukas P. Baumgartner, Franz Bethke, Andrea Walther · 2025
On the nonsmooth regularity condition LIKQ for different abs-normal representationsAbstract: Nonsmoothness is widely present in practical optimization problems for physical, technological, methodological, or numerical reasons, for example, due to modeling of valves or regularization with the ℓ 1 -norm.Many of these optimization problems can be described by a composition of smooth functions and the evaluations of the absolute value.Over the years, the precise definition of the resulting class of functions evolved also due to an improved understanding of such functions.This work analyzes the different representations of an element of this function class and the reformulation from one version to another.It is proved that the linear independent kink qualification (LIKQ) as one regularity condition needed for optimality conditions is preserved.Illustrative examples demonstrate comprehension and application of the results, elucidating the theoretical material.