Line search algorithms for locally Lipschitz functions on Riemannian manifolds
Line search algorithms for locally Lipschitz functions on Riemannian manifolds
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11.2016Verlag / herausgebende Einrichtung
Institut für Numerische Simulation (INS)Verlagsort
BonnMetadaten
Zur Langanzeige
Zitierbarer Link (Handle URI) 
https://hdl.handle.net/20.500.11811/11863
Inhalt
This paper presents line search algorithms for finding extrema of locally Lipschitz functions defined on Riemannian manifolds. To this end we generalize the so-called Wolfe conditions for nonsmooth functions on Riemannian manifolds. Using ε-subgradient-oriented descent directions and the Wolfe conditions, we propose a nonsmooth Riemannian line search algorithm and establish the convergence of our algorithm to a stationary point. Moreover, we extend the classical BFGS algorithm to nonsmooth functions on Riemannian manifolds. Numerical experiments illustrate the effectiveness and efficiency of the proposed algorithm.
Schlagwörter
Riemannian manifolds, Lipschitz functions, descent directions, Clarke subdifferential
Klassifikation (DDC)
510 Mathematik 518 Numerische AnalysisErstpublikation
https://ins.uni-bonn.de/publication/preprintsZugehörige Publikation(en)
https://doi.org/10.1137/16M1108145Reihe, Nummer
INS Preprints ; 1626Hosseini, Somayeh; Huang, Wen; Yousefpour, Rohollah: Line search algorithms for locally Lipschitz functions on Riemannian manifolds. In: INS Preprints, 1626.
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11863
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11863
@unpublished{handle:20.500.11811/11863,
author = {{Somayeh Hosseini} and {Wen Huang} and {Rohollah Yousefpour}},
title = {Line search algorithms for locally Lipschitz functions on Riemannian manifolds},
publisher = {Institut für Numerische Simulation (INS)},
year = 2016,
month = nov,
INS Preprints},
volume = 1626,
note = {This paper presents line search algorithms for finding extrema of locally Lipschitz functions defined on Riemannian manifolds. To this end we generalize the so-called Wolfe conditions for nonsmooth functions on Riemannian manifolds. Using ε-subgradient-oriented descent directions and the Wolfe conditions, we propose a nonsmooth Riemannian line search algorithm and establish the convergence of our algorithm to a stationary point. Moreover, we extend the classical BFGS algorithm to nonsmooth functions on Riemannian manifolds. Numerical experiments illustrate the effectiveness and efficiency of the proposed algorithm.},
url = {https://hdl.handle.net/20.500.11811/11863}
}
author = {{Somayeh Hosseini} and {Wen Huang} and {Rohollah Yousefpour}},
title = {Line search algorithms for locally Lipschitz functions on Riemannian manifolds},
publisher = {Institut für Numerische Simulation (INS)},
year = 2016,
month = nov,
INS Preprints},
volume = 1626,
note = {This paper presents line search algorithms for finding extrema of locally Lipschitz functions defined on Riemannian manifolds. To this end we generalize the so-called Wolfe conditions for nonsmooth functions on Riemannian manifolds. Using ε-subgradient-oriented descent directions and the Wolfe conditions, we propose a nonsmooth Riemannian line search algorithm and establish the convergence of our algorithm to a stationary point. Moreover, we extend the classical BFGS algorithm to nonsmooth functions on Riemannian manifolds. Numerical experiments illustrate the effectiveness and efficiency of the proposed algorithm.},
url = {https://hdl.handle.net/20.500.11811/11863}
}
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