Selime Gurol: September 7, 2012

The problem considered in this talk is the data assimilation problem arising in weather forecasting and oceanography, which consists in estimating the initial condition of a dynamical system whose future behaviour is to be predicted. More specifically, new optimization techniques will be discussed for the iterative solution of the particular nonlinear least-squares formulation of this inverse problem known under the name of 4DVAR, for four-dimensional data assimilation. These new methods are designed to decrease the computational cost in applications where the number of variables involved is expected to exceed $10^{^9}$. They involve the exploitation of the problem’s underlying geometrical structure in reformulating standard trust-region techniques into significantly cheaper variants. Adapted preconditioning issues for the considered systems of equations will be discussed, which also depend on the problem’s geometrical structure and which exploit limited-memory techniques in a novel way.