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Applications of Nonlinear Optimization Methods to the Study of Atmosphere Motion Predictability

Author: ZhangLei
Tutor: LiuYongMing
School: East China Normal University
Course: Applied Mathematics
Keywords: Unconstrained Optimization Conjugate Gradient Method Inexact line search Nonlinear optimization Predictability Disturbance
CLC: P456
Type: Master's thesis
Year: 2005
Downloads: 75
Quote: 0
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Abstract


This thesis is divided into two parts: the first part of an algorithm for solving large - scale nonlinear optimization problems , the algorithm is an inexact line search conjugate gradient method . It has the storage needs of small , fast convergence , is essentially a special kind of two - dimensional quasi-Newton method . It avoids the shortcomings of the conventional conjugate gradient method in solving nonlinear optimization problems . In the one-dimensional search using homogeneous function interpolation method to improve the convergence speed than the previous parabolic interpolation method . The numerical results show that this algorithm than the currently accepted value effect PRP method is generally more effective . The second part of this paper a more in-depth study of nonlinear optimal perturbation , the maximum principle usually use conditional nonlinear optimization problems into unconditional optimization problem to solve . According to this conclusion at the same time , through the variable transformation to reduce the dimension of the objective function of one-dimensional , and thus greatly reduce the amount of calculation and improve computational efficiency . Finally, the Lorenz equations , for example , the numerical solution of the corresponding nonlinear optimization problem , the optimization method is to take the first part of the amendment conjugate gradient method . Reveals the fundamental difference CNOP linear optimal perturbation .

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CLC: > Astronomy,Earth Sciences > Atmospheric science (meteorology ) > Weather Forecast > Forecasting Methods
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