A truncated Newton optimization algorithm in meteorology applications with analytic Hessian/vector products |
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Authors: | Zhi Wang I M Navon X Zou F X Le Dimet |
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Institution: | (1) Center for Analysis and Prediction of Storms, University of Oklahoma, 73019 Norman, OK;(2) Department of Mathematics and Supercomputer Computations, Research Institute, Florida State University, 32306 Tallahassee, FL;(3) National Center for Atmospheric Research, 80307 Boulder, Colorado;(4) Grenoble, Laboratoire de Modelisation et Calcul, B.P. 53X, 38041 Grenoble Cedex, France |
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Abstract: | A modified version of the truncated-Newton algorithm of Nash (24], 25], 29]) is presented differing from it only in the use of an exact Hessian vector product for carrying out the large-scale unconstrained optimization required in variational data assimilation. The exact Hessian vector products is obtained by solving an optimal control problem of distributed parameters. (i.e. the system under study occupies a certain spatial and temporal domain and is modeled by partial differential equations) The algorithm is referred to as the adjoint truncated-Newton algorithm. The adjoint truncated-Newton algorithm is based on the first and the second order adjoint techniques allowing to obtain a better approximation to the Newton line search direction for the problem tested here. The adjoint truncated-Newton algorithm is applied here to a limited-area shallow water equations model with model generated data where the initial conditions serve as control variables. We compare the performance of the adjoint truncated-Newton algorithm with that of the original truncated-Newton method 29] and the LBFGS (Limited Memory BFGS) method of Liu and Nocedal 23]. Our numerical tests yield results which are twice as fast as these obtained by the truncated-Newton algorithm and are faster than the LBFGS method both in terms of number of iterations as well as in terms of CPU time. |
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