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	Accelerated proximal gradient methods for nonconvex programming
	Li, Huan ; Lin, Zhouchen
	2015
英文摘要	Nonconvex and nonsmooth problems have recently received considerable attention in signal/image processing, statistics and machine learning. However, solving the nonconvex and nonsmooth optimization problems remains a big challenge. Accelerated proximal gradient (APG) is an excellent method for convex programming. However, it is still unknown whether the usual APG can ensure the convergence to a critical point in nonconvex programming. In this paper, we extend APG for general nonconvex and nonsmooth programs by introducing a monitor that satisfies the sufficient descent property. Accordingly, we propose a monotone APG and a nonmonotone APG. The latter waives the requirement on monotonic reduction of the objective function and needs less computation in each iteration. To the best of our knowledge, we are the first to provide APG-type algorithms for general nonconvex and nonsmooth problems ensuring that every accumulation point is a critical point, and the convergence rates remain O(1k2) when the problems are convex, in which k is the number of iterations. Numerical results testify to the advantage of our algorithms in speed.; EI; 379-387; 2015-January
语种	中文
出处	29th Annual Conference on Neural Information Processing Systems, NIPS 2015
内容类型	其他
源URL	[http://ir.pku.edu.cn/handle/20.500.11897/437004]
专题	信息科学技术学院
推荐引用方式 GB/T 7714	Li, Huan,Lin, Zhouchen. Accelerated proximal gradient methods for nonconvex programming. 2015-01-01.

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