Operations Research Transactions ›› 2011, Vol. ›› Issue (3): 9-18.

• Original Articles • Previous Articles     Next Articles

A class of limited memory BFGS-type algorithms for large-scale unconstrainedoptimization

 QIAN  Xiao-Yan, SHI  Qing-Sheng, LIU  Hao, SHI  Kui-Ran   

  • Received:2011-01-06 Revised:2011-05-26 Online:2011-09-15 Published:2011-09-29
  • Contact: Yan XiaoQIAN E-mail:xyqian122@163.com

Abstract: In this paper, objective function value information is exploited in limited memory BFGS-type algorithms. we first construct a new quadratic function satisfying some interpolation conditions to approximate the objective function, get a new weak secant equation. Combining the new weak secant equation and that obtained by Yuan\cite{yuan1991}, a class of limited memory BFGS--type algorithms including the classic LBFGS algorithm based on a new weak secant equation are proposed. The convergence of this class limited memory BFGS-type algorithms is proved. Numerical results for standard test problems from CUTE are reported, which indicate that all the algorithms in the proposed class perform quiet well.