W. W. Hager and H. C. Zhang, “Algorithm 851: CG DESCENT, A Conjugate Gradient Method with Guaranteed Descent,” ACM Transactions on Mathematical Software, Vol. 32, No. 1, 2006, pp. 113-137. doi:10.1145/1132973.1132979

has been cited by the following article:

• TITLE: Several New Line Search Methods and Their Convergence

  AUTHORS: Zhenjun Shi, Kimberly Kendricks, Zhiwei Xu, Yongning Tang

  KEYWORDS: Unconstrained Minimization; Line Search Method; Global Convergence; Convergence Rate

  JOURNAL NAME: American Journal of Operations Research, Vol.3 No.5, September 18, 2013

  ABSTRACT: In this paper, we propose several new line search rules for solving unconstrained minimization problems. These new line search rules can extend the accepted scope of step sizes to a wider extent than the corresponding original ones and give an adequate initial step size at each iteration. It is proved that the resulting line search algorithms have global convergence under some mild conditions. It is also proved that the search direction plays an important role in line search methods and that the step size approaches mainly guarantee global convergence in general cases. The convergence rate of these methods is also investigated. Some numerical results show that these new line search algorithms are effective in practical computation.