• Title/Summary/Keyword: unconstrained programme

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GLOBAL CONVERGENCE PROPERTIES OF THE MODIFIED BFGS METHOD ASSOCIATING WITH GENERAL LINE SEARCH MODEL

  • Liu, Jian-Guo;Guo, Qiang
    • Journal of applied mathematics & informatics
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    • v.16 no.1_2
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    • pp.195-205
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    • 2004
  • To the unconstrained programme of non-convex function, this article give a modified BFGS algorithm. The idea of the algorithm is to modify the approximate Hessian matrix for obtaining the descent direction and guaranteeing the efficacious of the quasi-Newton iteration pattern. We prove the global convergence properties of the algorithm associating with the general form of line search, and prove the quadratic convergence rate of the algorithm under some conditions.

GLOBAL CONVERGENCE OF A MODIFIED BFGS-TYPE METHOD FOR UNCONSTRAINED NON-CONVEX MINIMIZATION

  • Guo, Qiang;Liu, Jian-Guo
    • Journal of applied mathematics & informatics
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    • v.24 no.1_2
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    • pp.325-331
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    • 2007
  • 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 equation $B_{k+1}s_k=y^*_k,\;where\;y^*_k$ is the sum of $y_k\;and\;A_ks_k,\;and\;A_k$ is some matrix. The global convergence properties of the algorithm associating with the general form of line search is proved.

GLOBAL CONVERGENCE PROPERTIES OF TWO MODIFIED BFGS-TYPE METHODS

  • Guo, Qiang;Liu, Jian-Guo
    • Journal of applied mathematics & informatics
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    • v.23 no.1_2
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    • pp.311-319
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    • 2007
  • This article studies a modified BFGS algorithm for solving smooth unconstrained strongly convex minimization problem. The modified BFGS method is based on the new quasi-Newton equation $B_k+1{^s}_k=yk\;where\;y_k^*=yk+A_ks_k\;and\;A_k$ is a matrix. Wei, Li and Qi [WLQ] have proven that the average performance of two of those algorithms is better than that of the classical one. In this paper, we prove the global convergence of these algorithms associated to a general line search rule.