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Global convergence of a modified BFGS-type method for unconstrained non-convex minimization

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Abstract

To the unconstrained programme of non-convex function, this article give a modified BFGS algorithm associated with the general line search model. The idea of the algorithm is to modify the approximate Hessian matrix for obtaining the descent direction and guaranteeing the efficacious of the new quasi-Newton iteration equationB k +1s k =y *k ,, wherey *k is the sum ofy k andA k s k , andA k is some matrix. The global convergence properties of the algorithm associating with the general form of line search is proved.

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Authors and Affiliations

  1. Science College of Dalian Nationalities University, 116600, Dalian, P.R. China

    Qiang Guo

  2. Institute of System Engineering, Dalian University of Technology, 116024, Dalian, P. R. China

    Jian-Guo Liu

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  1. Qiang Guo
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  2. Jian-Guo Liu
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Correspondence to Jian-Guo Liu.

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Guo, Q., Liu, JG. Global convergence of a modified BFGS-type method for unconstrained non-convex minimization. J. Appl. Math. Comput. 24, 325–331 (2007). https://doi.org/10.1007/BF02832321

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  • DOI: https://doi.org/10.1007/BF02832321

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