Iteration Functions in Some Nonsmooth Optimization Algorithms

In this paper, it is proved that a locally Lipschitzian function has a PHR iteration function or a QS iteration function if and only if it is pseudo-regular, and a locally Lipschitzian function has a positive homogeneous PHR iteration function or a positive homogeneous QS iteration function if and only if it is continuously differentiable. In addition, we also give the computable PHR iteration functions or QS iteration functions for a piece-wise smooth function and a subsmooth function, respectively.