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An improved algorithm for L2-Lp minimization problem

Ge Dongdong(dongdong***at***gmail.com)
He Rongchuan(rongchuhe2***at***gmail.com)
He Simai (simaihe***at***mail.shufe.edu.cn)

Abstract: 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 epsilon-KKT point within O(log(1/epsilon)) iterations. The same result is also applied to the problem with general linear constraints under mild conditions.

Keywords: Nonsmooth optimization · Nonconvex optimization · Bridge Regression · Complexity analysis

Category 1: Global Optimization (Theory )

Category 2: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Category 3: Nonlinear Optimization (Unconstrained Optimization )

Citation: Submitted to Mathematical Programming. Shanghai University of Finance and Economics, June 2014

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Entry Submitted: 08/05/2014
Entry Accepted: 08/06/2014
Entry Last Modified: 08/05/2014

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