An improved algorithm for the L2 - Lp minimization problem

In this paper we consider a class of non-Lipschitz and non-convex minimization problems which generalize the L2 − Lp minimization problem. We propose an iterative algorithm that decides the next iteration based on the local convexity/concavity/sparsity of its current position. We show that our algorithm finds an -KKT point within O(log −1) iterations. The same result is also applied to the problem with general linear constraints under mild conditions.