Abstract
In this paper, we present an analysis about the rate of convergence of an inexact proximal point algorithm to solve minimization problems for quasiconvex objective functions on Hadamard manifolds. We prove that under natural assumptions the sequence generated by the algorithm converges linearly or superlinearly to a critical point of the problem.
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This work was supported by Coordenação de Aperfeiçoamento de Pessoal de Nível Superior of the Federal University of Rio de Janeiro (UFRJ), Brazil.
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Baygorrea, N., Papa Quiroz, E.A. & Maculan, N. On the Convergence Rate of an Inexact Proximal Point Algorithm for Quasiconvex Minimization on Hadamard Manifolds. J. Oper. Res. Soc. China 5, 457–467 (2017). https://doi.org/10.1007/s40305-016-0129-z
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DOI: https://doi.org/10.1007/s40305-016-0129-z
Keywords
- Proximal point method
- Quasiconvex function
- Hadamard manifolds
- Nonsmooth optimization
- Abstract subdifferential
- Convergence rate