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

Abstract

It has proved that non-convex optimization with the feasible set satisfying quasi-normal cone condition (QNCC) can be solved by the method of Homotopy Interior Point (HIP) Method with global convergence under the hypothesis that a quasi-normal cone has been constructed. 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 construct HIP function and realize the HIP method algorithms. And we prove it is available by the numerical example at the same time.