Line Search Algorithms for Locally Lipschitz Functions on Riemannian Manifolds
Authors
Somayeh Hosseini, Wen Huang, and Roholla Yousefpour
Abstract
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 ŠĆ-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.
Status
SIAM Journal on Optimization, 28(1), pp. 596-619.
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- Technical report: PDF
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- Experiment code: Code
BibTex entry
- Technical Report
@TECHREPORT{HAG2015,
author = "S. Hosseini and W. Huang and R. Yousefpour",
title = "Line Search Algorithms for Locally Lipschitz Functions on Riemannian Manifolds",
institution = "Institut f\"ur Numerische Simulation",
number = "INS Preprint No. 1626",
year = 2016,
}