Approximate necessary optimality conditions in terms of Fréchet subgradients and normals for a general optimization problem with a potentially non-Lipschitzian objective function are discussed. The main tools are Ekeland variational principle, the fuzzy Fréchet subdifferential sum rule, and a novel notion of lower semicontinuity relative to a set.
Kruger, A. Y. and Mehlitz, P.: Optimality conditions, approximate stationarity, and applications – a story beyond Lipschitzness. arXiv 2110.07268 (2021).
The research is supported by the Australian Research Council, project DP160100854.