Two modified HS type conjugate gradient methods for unconstrained optimization problems |
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Authors: | Zhi-Feng Dai |
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Institution: | College of Mathematics and Econometrics, Hunan University, Changsha, 410082, China College of Mathematics and Computational Science, Changsha University of Science and Technology, Changsha 410014, China |
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Abstract: | Based on the modified secant equation, we propose two new HS type conjugate gradient formulas. Their forms are similar to the original HS conjugate gradient formula and inherit all nice properties of the HS method. By utilizing the technique of the three-term HS method in Zhang et al. (2007) 15], without the requirement of truncation and convexity of the objective function, we show that one with Wolfe line search and the other with Armijo line search are globally convergent. Moreover, under some mild conditions, the linear convergence rate of the two modified methods is established. The numerical results show that the proposed methods are efficient. |
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Keywords: | 49M37 90C30 65K05 |
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