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In this study we present a semi-local convergence analysis of the Gauss-Newton method for solving convex composite optimization problems in Riemannian manifolds using the our idea of restricted convergence domains. Using this idea we introduce majorizing sequences for the Gauss-Newton method that are more precise than in earlier studies. Consequently, our semi-local convergence analysis for the Gauss-Newton method has the following advantages under the same computational cost: weaker sufficient convergence conditions; more precise estimates on the distances involved and an at least as precise information on the location of the solution.
How to Cite this Article:
Ioannis K. Argyros, Santhosh George, Extending the applicability of Gauss-Newton method for convex composite optimization on Riemannian manifolds using restricted convergence domains, Journal of Nonlinear Functional Analysis 2016 (2016), Article ID 27.