We study weak sharp minima for optimization problems with cone constraints. Some necessary conditions for weak sharp minima of higher order are established by means of upper Studniarski or Dini directional derivatives. In particular, when the objective and constrained functions are strict derivative, a necessary condition is obtained by a normal cone.
Zhang, W. Y., Xu, S., & Li, S. J. (2012). Necessary Conditions for Weak Sharp Minima in Cone-Constrained Optimization Problems. Abstract and Applied Analysis, 2012, 1–11. https://doi.org/10.1155/2012/909520