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A Riemannian subspace limited-memory SR1 trust region method

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Abstract

In this paper, we present a new trust region algorithm on any compact Riemannian manifolds using subspace techniques. The global convergence of the method is proved and local \(d+1\)-step superlinear convergence of the algorithm is presented, where d is the dimension of the Riemannian manifold. Our numerical results show that the proposed subspace algorithm is competitive to some recent developed methods, such as the LRTR-SR1 method, the LRTR-BFGS method, the Riemannian CG method.

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Acknowledgments

The work of Wei Hong Yang was supported by the National Natural Science Foundation of China No. 11371102 and NSFC Key Project 91330201.

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Authors and Affiliations

  1. School of Mathematical Sciences, Fudan University, 220 Handan Road, Shanghai, 200433, China

    Hejie Wei & Wei Hong Yang

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  1. Hejie Wei
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  2. Wei Hong Yang
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Correspondence to Hejie Wei.

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Wei, H., Yang, W.H. A Riemannian subspace limited-memory SR1 trust region method. Optim Lett 10, 1705–1723 (2016). https://doi.org/10.1007/s11590-015-0977-1

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  • DOI: https://doi.org/10.1007/s11590-015-0977-1

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