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• W2177964621 abstract "This paper presents a Riemannian trust region algorithm for unconstrained optimization problems with locally Lipschitz objective functions defined on complete Riemannian manifolds. To this end we define a function |$Phi :TMrightarrow mathbb {R}$| on the tangent bundle |$TM$|⁠, and at the |$k$|th iteration, using the restricted function |$Phi |_{T_{x_k}M}$|⁠, where |$T_{x_k}M$| is the tangent space at |$x_k$|⁠, a local model function |$Q_k$| that carries both first- and second-order information for the locally Lipschitz objective function |$f:Mrightarrow mathbb {R}$| on a Riemannian manifold |$M$|⁠, is defined and minimized over a trust region. We establish the global convergence of the proposed algorithm. Moreover, using the Riemannian |$varepsilon $|-subdifferential, a suitable model function is defined. Numerical experiments illustrate our results." @default.
• W2177964621 created "2016-06-24" @default.
• W2177964621 creator A5023888160 @default.
• W2177964621 creator A5086940784 @default.
• W2177964621 date "2015-09-14" @default.
• W2177964621 modified "2023-10-16" @default.
• W2177964621 title "Nonsmooth trust region algorithms for locally Lipschitz functions on Riemannian manifolds" @default.
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• W2177964621 doi "https://doi.org/10.1093/imanum/drv043" @default.
• W2177964621 hasPublicationYear "2015" @default.
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