The Riemannian Barzilai-borwein Method with Nonmonotone Line-search and the Karcher Mean Computation∗
نویسندگان
چکیده
The Barzilai-Borwein method for nonlinear optimization is adapted 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 BarzilaiBorwein method with nonmonotone line-search is shown to be competitive in several Riemannian optimization problems. When used to compute the Karcher mean of positive definite matrices, it notably outperforms existing first-order optimization methods.
منابع مشابه
The Riemannian Barzilai-borwein Method with Nonmonotone Line-search and the Matrix Geometric Mean Computation
The Barzilai-Borwein method, an effective gradient descent method with cleaver 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 Barzilai-Borwein...
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