A method to construct a quasi-normal cone for non-convex and non-smooth set and its applications to non-convex and non-smooth optimization

If the feasible set of non-convex optimization satisfies quasi-normal cone condition (QNCC) and under the hypothesis that a quasi-normal cone has been constructed, non-convex optimizations can be solved, theoretically, by the method of Homotopy Interior Point (HIP) Method with global convergence. But how to construct the quasi-normal cone for a general non-convex set is very difficult and there is no uniform and efficient method to do it. In this paper, we give a method to construct a quasi-normal cone for a class of sets satisfying QNCC, and realize HIP method algorithms under it. And we prove it is available by the numerical example at the same time.