Nonsmooth nonconvex optimization on Riemannian manifolds via bundle trust region algorithm

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...

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Bibliographic Details
Published in:Computational optimization and applications 2024-07, Vol.88 (3), p.871-902
Main Authors: Hoseini Monjezi, N., Nobakhtian, S., Pouryayevali, M. R.
Format: Article
Language:English
Subjects:
Applied mathematics
Convex and Discrete Geometry
Iterative algorithms
Management Science
Mathematics
Mathematics and Statistics
Methods
Operations Research
Operations Research/Decision Theory
Optimization
Optimization algorithms
Optimization techniques
Riemann manifold
Statistics
Topological manifolds
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Summary: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.
ISSN:0926-6003
1573-2894
DOI:10.1007/s10589-024-00569-5