Optimality conditions for mildly nonsmooth constrained optimization

摘要

We study necessary optimality conditions for constrained minimization problems involving nonsmooth functions. We restrict our attention to a class of functions we call directionally steady functions for which these optimality conditions can be written in simple terms. This class encompasses the class of locally Lipschitzian functions and the class of directionally differentiable functions and it enjoys useful stability properties under usual operations. We also compare our stability property with epi-differentiability