On the robust isolated calmness of a class of nonsmooth optimizations on Riemannian manifolds and its applications

Chenglong Bao (), Chao Ding () and Yuexin Zhou ()
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Chenglong Bao: Tsinghua University
Chao Ding: State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences
Yuexin Zhou: University of Chinese Academy of Sciences

Computational Optimization and Applications, 2025, vol. 92, issue 2, No 11, 709-754

Abstract: Abstract This paper studies the robust isolated calmness property of the KKT solution mapping of a class of nonsmooth optimization problems on Riemannian manifolds. The manifold versions of the Robinson constraint qualification, the strict Robinson constraint qualification, and the second order conditions are defined and discussed. We show that the robust isolated calmness of the KKT solution mapping is equivalent to satisfying the M-SRCQ and M-SOSC conditions. Furthermore, under the above two conditions, we show that the Riemannian augmented Lagrangian method achieves a local linear convergence rate. Finally, we verify the proposed conditions and demonstrate the convergence rate on two minimization problems over the sphere and the manifold of fixed rank matrices.

Keywords: Nonsmooth optimizations; Riemannian manifolds; Robust isolated calmness; Augmented Lagrangian method; Rate of convergence; 90C30; 90C31; 49J52; 65K05 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10589-025-00712-w

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