Open AccessThe spectral conjugate gradient method in variational adjoint assimilation for model terrain correction II: Numerical test
Author(s) -
Sulin Tao,
Yuhong Li,
Isaac Mugume,
Shuanghe Shen
Publication year - 2020
Publication title -
iop conference series. materials science and engineering
Language(s) - English
Resource type - Journals
eISSN - 1757-899X
pISSN - 1757-8981
DOI - 10.1088/1757-899x/768/7/072043
Subject(s) - conjugate gradient method , line search , mathematics , nonlinear conjugate gradient method , gradient descent , regularization (linguistics) , extrapolation , interpolation (computer graphics) , algorithm , mathematical optimization , mathematical analysis , computer science , animation , computer graphics (images) , computer security , machine learning , artificial intelligence , artificial neural network , radius
The performance of the spectral conjugate gradient (SCG) method proposed in part I of this paper is evaluated by comparison with that of the limited-memory Broyden-Fletcher-Goldfarb-Shanno (LBFGS) method and Hager and Zhang’s CG_DESCENT method. The step length is determined by solving the tangent linear model and a line search algorithm with cubic interpolation is introduced for comparison. Numerical tests indicate that the SCG method is effective at correcting the bottom terrain. It is robust, providing small root mean square (RMS) errors and smooth profiles for the corrected bottom terrain for all tests conducted. It has much higher optimizing efficiency than Hager and Zhang’s CG_DESCENT and Liu’s LBFGS methods. The SCG method reduces the norm of the gradient sufficiently and the value of the cost function very quickly. It always provides linear convergence rates, especially when including a regularization term. This study suggests the combined utilization of the SCG method and line search strategy to ensure high efficiency when solving the large-scale unconstrained problems.