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• W2789764089 abstract "The Barzilai–Borwein (BB) method, an effective gradient descent method with clever choice of the step length, is adapted from nonlinear optimization to Riemannian manifold optimization. More generally, global convergence of a nonmonotone line search strategy for Riemannian optimization algorithms is proved under some standard assumptions. By a set of numerical tests, the Riemannian BB method with nonmonotone line search is shown to be competitive in several Riemannian optimization problems. When used to compute the matrix geometric mean, known as the Karcher mean of positive definite matrices, it notably outperforms existing first-order optimization methods." @default.
• W2789764089 created "2018-03-29" @default.
• W2789764089 creator A5036085823 @default.
• W2789764089 creator A5044580481 @default.
• W2789764089 date "2017-04-10" @default.
• W2789764089 modified "2023-10-01" @default.
• W2789764089 title "The Riemannian Barzilai–Borwein method with nonmonotone line search and the matrix geometric mean computation" @default.
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• W2789764089 doi "https://doi.org/10.1093/imanum/drx015" @default.
• W2789764089 hasPublicationYear "2017" @default.
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