A Conjugate Gradient Method Based on a Modified Secant Relation for Unconstrained Optimization

Based on the modified secant relation given by Zhang and Xu and making use of the Dai and Liao approach, Babaie-Kafaki et al. presented a conjugate gradient method to solve unconstrained optimization. In this paper, we made some modifications on the conjugate gradient parameter proposed by Babaie-Kafaki et al. and obtained some attractive results in theory and practice. Under appropriate conditions, we show that the proposed method is globally convergent without needing convexity assumption on the objective function. Comparative results show computational efficiency of the proposed method in the sense of the Dolan-Moré performance profiles.