Fusion Adaptive Conjugate Gradient Method And Multidimensional Filter Method Solving Unconstrained Optimization Problems

This paper which is consisted of the following two parts mainly discusses unconstrained optimization problems. The first part offers a new conjugate gradient algorithm to solve unconstrained optimization problems. The conjugate gradient algorithm is provided on the basis of that of Zhifen Dai and Boshi Tian, and is actually a common methods, for example, the three modified parameters from Gonglin Yuan βkDPRP,βkDLS and βkDHS are only particular cases. Under hypothesis of uniform convex of objective function and positive parameter βk this common algorithm is convergence globally. Its experiments show the good effect of βkDHS algorithm.The other part of this paper provides a new kind of linear search filter algorithm with the latest multi-filter for solving unconstrained optimization problems. New switching criterion of this new algorithm is set on the base of conjugate gradient algorithm and negative gradient provided in the first part. This criterion will restart the conjugate gradient algorithm, and the adaptive is realized. The algorithm, under general hypothesis, is proved to converge to critical points of objective function, and its experiment shows that the algorithm is efficient.