The Improvement of Newton Method and the Validation of Optimization Idea of Blind Walking Repeatedly
The existence of maximum point, oddity point and saddle point often leads to computation failure. The optimization idea is based on the reality that the optimum towards the local minimum related the initial point. After getting several optimal results with different initial point, the best result is taken as the final optimal result. The arithmetic improvement of multi-dimension Newton method is improved. The improvement is important for the optimization method with grads convergence rule or searching direction constructed by grads. A computational example with a saddle point, maximum point and oddity point is studied by multi-dimension Newton method, damped Newton method and Newton direction method. The importance of the idea of blind walking repeatedly is testified. Owing to the parallel arithmetic of modernistic optimization method, it does not need to study optimization problem with seriate feasible domain by modernistic optimization method.
Guangfan Li, Yong Huang and Chaohe Chen
C. L. Zhang "The Improvement of Newton Method and the Validation of Optimization Idea of Blind Walking Repeatedly", Advanced Materials Research, Vols. 250-253, pp. 4061-4064, 2011