Gauss–Newton method for convex composite optimizations on Riemannian manifolds
Gauss–Newton method for convex composite optimizations on Riemannian manifolds
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DOI：
10.1007/s10898-010-9638-1
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发表时间：
2012-05
影响因子：
1.8
通讯作者：
Jinhua Wang;J. Yao;Chong Li
中科院分区：
文献类型：
--
作者：
Jinhua Wang;J. Yao;Chong Li
将拟正则性的概念推广到包含问题，其中F是从黎曼流形M到的可微映射。当C是凸实函数的极小点集，且DF满足l-平均Lipschitz条件时，我们利用优超函数技巧建立了◦Fon黎曼流形上由高斯-牛顿法(具有拟正则初始点)生成的序列的半局部收敛.给出了两种应用：一种是黎曼流形上的正则性，另一种是C是锥且DF(P_0)(·)−是满射的情形。特别地，本文所得结果推广了Wang等人的相应结果。(台湾数学杂志13：633-656,2009)。
A notion of quasi-regularity is extended for the inclusion problem, whereFis a differentiable mapping from a Riemannian manifoldMto. WhenCis the set of minimum points of a convex real-valued functionhonand DFsatisfies theL-average Lipschitz condition, we use the majorizing function technique to establish the semi-local convergence of sequences generated by the Gauss-Newton method (with quasi-regular initial points) for the convex composite functionh◦Fon Riemannian manifold. Two applications are provided: one is for the case of regularities on Riemannian manifolds and the other is for the case whenCis a cone and DF(p0)(·) −Cis surjective. In particular, the results obtained in this paper extend the corresponding one in Wang et al. (Taiwanese J Math 13:633–656, 2009).