Abstract
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.
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