Nonsmooth nonconvex optimization on Riemannian manifolds via bundle trust region algorithm

N. Hoseini Monjezi (), S. Nobakhtian () and M. R. Pouryayevali ()
Additional contact information
N. Hoseini Monjezi: University of Isfahan
S. Nobakhtian: University of Isfahan
M. R. Pouryayevali: University of Isfahan

Computational Optimization and Applications, 2024, vol. 88, issue 3, No 6, 902 pages

Abstract: 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.

Keywords: Riemannian optimization; Trust region method; Bundle algorithm; Locally Lipschitz functions; Clarke subdifferential; 65K05; 58C05; 49J52 (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10589-024-00569-5 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:coopap:v:88:y:2024:i:3:d:10.1007_s10589-024-00569-5

Ordering information: This journal article can be ordered from
http://www.springer.com/math/journal/10589

DOI: 10.1007/s10589-024-00569-5

Access Statistics for this article

Computational Optimization and Applications is currently edited by William W. Hager

More articles in Computational Optimization and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().