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**A truncated Newton optimization algorithm in meteorology applications with analytic Hessian/vector products.**
*(English)*
Zbl 0831.90124

Summary: A modified version of the truncated-Newton algorithm of S. G. Nash [SIAM J. Sci. Stat. Comput. 6, 599-616 (1985; Zbl 0592.65038)] 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 product 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 and the LBFGS (Limited Memory BFGS)method of D. C. Liu and J. Nocedal [Math. Program., Ser. B 45, No. 3, 503-528 (1989; Zbl 0696.90048)]. 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.

### MSC:

90C52 | Methods of reduced gradient type |

90C90 | Applications of mathematical programming |

86A10 | Meteorology and atmospheric physics |

90C30 | Nonlinear programming |

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\textit{Z. Wang} et al., Comput. Optim. Appl. 4, No. 3, 241--262 (1995; Zbl 0831.90124)

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### References:

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