Gauss---Newton method for convex composite optimizations on Riemannian manifolds

  • Authors:

  • Jin-Hua Wang;Jen-Chih Yao;Chong Li

  • Affiliations:

  • Department of Mathematics, Zhejiang University of Technology, Hangzhou, People's Republic of China 310032;Department of Mathematics, National Sun Yat-sen University, Kaohsiung, Taiwan;Department of Mathematics, Zhejiang University, Hangzhou, People's Republic of China 310027 and Department of Mathematics, College of Sciences, King Saud University, Riyadh, Saudi Arabia 11451

  • Venue:
  • Journal of Global Optimization
  • Year:
  • 2012

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Abstract

A notion of quasi-regularity is extended for the inclusion problem $${F(p)\in C}$$ , where F is a differentiable mapping from a Riemannian manifold M to $${\mathbb R^n}$$ . When C is the set of minimum points of a convex real-valued function h on $${\mathbb R^n}$$ and DF satisfies the L-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 function h 驴 F on Riemannian manifold. Two applications are provided: one is for the case of regularities on Riemannian manifolds and the other is for the case when C is a cone and DF(p 0)(·) 驴 C is surjective. In particular, the results obtained in this paper extend the corresponding one in Wang et al. (Taiwanese J Math 13:633---656, 2009).