Speaker: Bruno Iannazzo Affiliation: Università di Perugia, Italy Time: Thursday 2017-08-27, h. 11:00 Place: Sala Seminari Est, Dipartimento di Informatica, Università di Pisa Title: The Riemannian Barzilai-Borwein algorithm and the matrix geometric mean computation

Abstract: We consider the problem of computing the geometric mean of positive definite matrices, the so-called Karcher mean. For this purpose, we adapt the Barzilai-Borwein method from nonlinear optimization to Riemannian manifold optimization. Incomporating a nonmonotone line-search strategy yields global convergence under standard assumptions, fulfilled in the problem of the matrix geometric mean. By a set of numerical tests, we show that the Riemannian Barzilai-Borwein method notably outperforms existing first-order optimization methods for computing the matrix geometric mean.

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Everyone is welcome. Sorry for the short notice!