Speaker
Description
Abs-smooth optimization problems consist of objective functions, and possibly constraints, that are build as finite compositions of smooth elementals and the absolute value function. These optimization problems can be written in the so-called abs-normal form by replacing all arguments of the absolute value by new variables and adding these relations as an additional constraint called switching equation to the problem. The linear independence kink qualification (LIKQ) plays an important role in the analysis of abs-smooth optimization problems in abs-normal form. In particular, provided that LIKQ holds it is possible to derive optimality conditions for abs-smooth optimization problems that can be checked in polynomial time.The talk focuses on the question of how stringent the LIKQ assumption is. Using a generalization of the classical jet transversality theorem it can be shown that the subset of problems that satisfy the LIKQ condition at all feasible points is dense and open with respect to the strong Whitney topology.
