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Optim."],"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p>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 $\\varepsilon$-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.<\/jats:p>","DOI":"10.1137\/16m1108145","type":"journal-article","created":{"date-parts":[[2018,3,7]],"date-time":"2018-03-07T11:05:59Z","timestamp":1520420759000},"page":"596-619","source":"Crossref","is-referenced-by-count":58,"title":["Line Search Algorithms for Locally Lipschitz Functions on Riemannian Manifolds"],"prefix":"10.1137","volume":"28","author":[{"given":"S.","family":"Hosseini","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"W.","family":"Huang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"R.","family":"Yousefpour","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2018,3,6]]},"reference":[{"key":"atypb1","doi-asserted-by":"crossref","unstructured":"P. A. Absil, R. Mahony, and R. 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(2010), pp. 564-572.","DOI":"10.1016\/j.na.2010.03.057"},{"key":"atypb7","unstructured":"G. Dirr, U. Helmke, and C. Lageman,\n                      Nonsmooth Riemannian optimization with applications to sphere packing and grasping\n                      , in Lagrangian and Hamiltonian Methods for Nonlinear Control 2006: Proceedings from the 3rd IFAC Workshop, Nagoya, Japan, 2006, Lecture Notes in Control and Inform. Sci., 366, Springer, New York, 2007."},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1007\/BF00934767"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1007\/s10444-015-9426-z"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1093\/imanum\/drv043"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2011.02.023"},{"key":"atypb12","first-page":"67","volume":"20","author":"Hosseini S.","year":"2013","journal-title":"J. Convex. 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Lee,\n                      Geometric Optimization for Computer Vision,\n                      Ph.D. thesis, Australian National University, 2005."},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-012-0514-2"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1137\/09075367X"},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-012-0024-7"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1287\/moor.2.2.191"},{"key":"atypb25","doi-asserted-by":"crossref","unstructured":"J. Nocedal and S. J. 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