Asymptotic regularity for Lipschitzian nonlinear optimization problems with applications to complementarity constrained and bilevel programming

Asymptotic stationarity and regularity conditions turned out to be quite useful study the qualitative properties of numerical solution methods for standard nonlinear complementarity constrained programs. In this paper, we first extend these notions optimization problems with nonsmooth but Lipschitzian data functions in order find reasonable asymptotic terms Clarke's Mordukhovich's subdifferential construction. Particularly, compare associated novel constraint qualifications already existing ones. The second part paper presents two applications obtained theory. On one hand, specify our findings recover recent results from literature which demonstrates power approach. Furthermore, hint at potential extensions or- vanishing optimization. other demonstrate usefulness context bilevel More precisely, justify a well-known system affinely way. Afterwards, suggest algorithm class combines penalty method ideas DC-programming. After brief convergence analysis, present some experiments.