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Cheng-xian Xu Yue-ting Yang 《计算数学(英文版)》2005,23(4):357-372
Convergence properties of a class of multi-directional parallel quasi-Newton algorithmsfor the solution of unconstrained minimization problems are studied in this paper.At eachiteration these algorithms generate several different quasi-Newton directions,and thenapply line searches to determine step lengths along each direction,simultaneously.Thenext iterate is obtained among these trail points by choosing the lowest point in the sense offunction reductions.Different quasi-Newton updating formulas from the Broyden familyare used to generate a main sequence of Hessian matrix approximations.Based on theBFGS and the modified BFGS updating formulas,the global and superlinear convergenceresults are proved.It is observed that all the quasi-Newton directions asymptoticallyapproach the Newton direction in both direction and length when the iterate sequenceconverges to a local minimum of the objective function,and hence the result of superlinearconvergence follows. 相似文献