Nondifferentiable multiplier rules for optimization and bilevel optimization problems

In this paper we study optimization problems with equality and inequality constraints on a Banach space where the objective function and the binding constraints are either differentiable at the optimal solution or Lipschitz near the optimal solution. Necessary and sufficient optimality conditions and constraint qualifications in terms of the Michel-Penot subdifferential are given, and the results are applied to bilevel optimization problems.