Proximal gradient algorithm with trust region scheme on Riemannian manifold

Shimin Zhao (), Tao Yan () and Yuanguo Zhu ()
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Shimin Zhao: Nanjing University of Science and Technology
Tao Yan: Nanjing University of Science and Technology
Yuanguo Zhu: Nanjing University of Science and Technology

Journal of Global Optimization, 2024, vol. 88, issue 4, No 10, 1076 pages

Abstract: Abstract We consider the problem of minimizing the sum of a smooth function and nonsmooth function over a Riemannian manifold. We develop a Riemannian proximal gradient algorithm with a trust region scheme for the problem. Global convergence is presented under natural assumptions. We establish an $$O(1/{\varepsilon ^2})$$ O ( 1 / ε 2 ) iteration complexity bound that matches the best-known complexity bound of Riemannian trust region methods for smooth optimization. Moreover, we give a nonmonotone version and an accelerated version of the Riemannian proximal gradient algorithm with a trust region scheme. Their global convergence is established. Numerical results demonstrate the effectiveness of the proposed methods.

Keywords: Riemannian optimization; Riemannian proximal gradient method; Trust region methods; Nonmonotone; Oblique manifold; Stiefel manifold (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10898-023-01326-4

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