Accelerate The Convergence Of Nonlinear Optimization And Its Applications

Accelerated convergence method for sequence can use less computation to get numerical result accurately and quickly. For this reason, it was wildly used in every branch of numerical computation. Based on this idea, we discuss the solution of nonlinear optimization.First, we discuss the one dimension search which is the main part of nonlinear optimization, and we get three accelerated one dimension search algorithms. To interpret our result, we not only give the theoretical proofs, but also give some numerical experiments.Second, For vector sequence coming from the steep-descent method, we use extrapolation method for the sequence and get some applied algorithms. We also give theoretical proofs for this algorithms. Many numerical experiments tell us that the new algorithms sometimes can save 80% computation.In the last of this paper we apply our algorithms to the learning of feed-forward neural network, and get some new learning algorithms. We also give some numerical experiments to compare our algorithms with others...