Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
권호 표지

GLOBAL CONVERGENCE PROPERTIES OF TWO MODIFIED BFGS-TYPE METHODS

  • Guo, Qiang (Science College of Dalian Natyionalities University) ;
  • Liu, Jian-Guo (Institute of System Engineering, Dalian University of Technology)
  • Published : 2007.01.31

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Abstract

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.

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