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Nonsmooth nonconvex optimization on Riemannian manifolds via bundle trust region algorithm

Author

Listed:
  • N. Hoseini Monjezi

    (University of Isfahan)

  • S. Nobakhtian

    (University of Isfahan)

  • M. R. Pouryayevali

    (University of Isfahan)

Abstract

This paper develops an iterative algorithm to solve nonsmooth nonconvex optimization problems on complete Riemannian manifolds. The algorithm is based on the combination of the well known trust region and bundle methods. According to the process of the most bundle methods, the objective function is approximated by a piecewise linear working model which is updated by adding cutting planes at unsuccessful trial steps. Then at each iteration, by solving a subproblem that employs the working model in the objective function subject to the trust region, a candidate descent direction is obtained. We study the algorithm from both theoretical and practical points of view and its global convergence is verified to stationary points for locally Lipschitz functions. Moreover, in order to demonstrate the reliability and efficiency, a MATLAB implementation of the proposed algorithm is prepared and results of numerical experiments are reported.

Suggested Citation

  • N. Hoseini Monjezi & S. Nobakhtian & M. R. Pouryayevali, 2024. "Nonsmooth nonconvex optimization on Riemannian manifolds via bundle trust region algorithm," Computational Optimization and Applications, Springer, vol. 88(3), pages 871-902, July.
    • Handle: RePEc:spr:coopap:v:88:y:2024:i:3:d:10.1007_s10589-024-00569-5
    DOI: 10.1007/s10589-024-00569-5
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    References listed on IDEAS

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    1. Yang Yang & Liping Pang & Xuefei Ma & Jie Shen, 2014. "Constrained Nonconvex Nonsmooth Optimization via Proximal Bundle Method," Journal of Optimization Theory and Applications, Springer, vol. 163(3), pages 900-925, December.
    2. N. Hoseini Monjezi & S. Nobakhtian, 2022. "An inexact multiple proximal bundle algorithm for nonsmooth nonconvex multiobjective optimization problems," Annals of Operations Research, Springer, vol. 311(2), pages 1123-1154, April.
    3. O. Ferreira & A. Iusem & S. Németh, 2014. "Concepts and techniques of optimization on the sphere," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 1148-1170, October.
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    5. Glaydston Carvalho Bento & Sandro Dimy Barbosa Bitar & João Xavier Cruz Neto & Paulo Roberto Oliveira & João Carlos Oliveira Souza, 2019. "Computing Riemannian Center of Mass on Hadamard Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 183(3), pages 977-992, December.
    6. G. C. Bento & O. P. Ferreira & P. R. Oliveira, 2012. "Unconstrained Steepest Descent Method for Multicriteria Optimization on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 154(1), pages 88-107, July.
    7. W. Hare & C. Sagastizábal & M. Solodov, 2016. "A proximal bundle method for nonsmooth nonconvex functions with inexact information," Computational Optimization and Applications, Springer, vol. 63(1), pages 1-28, January.
    8. Najmeh Hoseini Monjezi & S. Nobakhtian, 2019. "A new infeasible proximal bundle algorithm for nonsmooth nonconvex constrained optimization," Computational Optimization and Applications, Springer, vol. 74(2), pages 443-480, November.
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