Following recent attempts to find appropriate choices for parameter of the nonlinear conjugate gradient method proposed by Dai and Liao, two adaptive versions of the method are proposed based on a matrix analysis and using the memoryless BFGS updating formula. Under proper conditions, it is shown that the methods are globally convergent. Numerical experiments are done on a set of CUTEr unconstrained optimization test problems; they demonstrate the efficiency of the proposed methods in the sense of Dolan–Moré performance profile.
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The authors are grateful to Professor William W. Hager for providing the line search code. They also thank the anonymous reviewer for his/her valuable suggestions helped to improve the presentation.
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Babaie-Kafaki, S., Ghanbari, R. Two Adaptive Dai–Liao Nonlinear Conjugate Gradient Methods. Iran J Sci Technol Trans Sci 42, 1505–1509 (2018). https://doi.org/10.1007/s40995-017-0271-4
- Unconstrained optimization
- Conjugate gradient method
- BFGS update
- Line search
- Global convergence
Mathematics Subject Classification