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	Determining step sizes in geometric optimization algorithms
	Li, Zhizhong ; Zhao, Deli ; Lin, Zhouchen ; Chang, Edward Y.
	2015
英文摘要	Optimization on Riemannian manifolds is an intuitive generalization of the traditional optimization algorithms in Euclidean spaces. In these algorithms, minimizing along a search direction becomes minimizing along a search curve lying on a manifold. Computing such a curve to be subsequently searched upon is itself computational intensive. We propose a new minimization scheme aiming to find a better step size utilizing the first order information of the search curve. We prove that this scheme can provide further reduction for the cost function when the retraction and the vector transport are collinear. Then we adapt this scheme to propose a heuristic strategy for line search. In numerical experiments, we apply this heuristic strategy to one of the geometric algorithms for matrix completion and show its feasibility and the potential in accelerating computation. ? 2015 IEEE.; EI; 1217-1221; 2015-June
语种	英语
出处	EI
出版者	IEEE International Symposium on Information Theory, ISIT 2015
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/436620]
专题	数学科学学院 信息科学技术学院
推荐引用方式 GB/T 7714	Li, Zhizhong,Zhao, Deli,Lin, Zhouchen,et al. Determining step sizes in geometric optimization algorithms. 2015-01-01.

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