Applications Of Nonlinear Optimization Methods To The Study Of Atmosphere Motion Predictability

This paper is separated into two parts:In the first part, an algorithm for solving large scale nonlinear optimization problems is described. It is a conjugate gradient method by using inexact line search. By virtue of their storage saving properties and greatly convergence rate, it is a special 2-dirnension quasi-Newton method in essence.With homogeneous function interpolation instead of parabolic interpolation, the algorithm can be greatly accelerated convergence rate by inexact line search. The new algorithm avoids some shortcoming existed in common conjugate gradient method.In this paper, the new algorithm is compared numerically with another conjugate gradient method. The results of numerical tests indicate that it is a good algorithm than the PRP+ algorithm.In the second part, we have a further research to nonlinear optimum perturbation and describe the maximal principle. It can transform the problem of conditional optimization to the problem of non-condtional optimization. On the basis of this theory, we make the dimension of the object function down and improve the computational efficiency by using the transformation of variations. At last, we choose Lorenz equation as an example. The method of optimization we prefered is conjugate gradient method in the first part. The nonlinear characteristics of the model are disclosed not only from the initial patterns but also from the nonlinear evolution.