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Two modified Polak-Ribi√®re-Polyak-type nonlinear conjugate methods with sufficient descent property. (English) Zbl 1202.90239

Summary: We propose a new conjugate gradient type formula for computing unconstrained optimization problems. Its form is similar to the original PRP formula and it inherits all nice properties of the PRP method. By utilizing the technique of the three-term PRP method of L. Zhang, W. Zhou and D. Li [IMA J. Numer. Anal. 26, No. 4, 629–640 (2006; Zbl 1106.65056)] and the modified PRP method of G. H. Yu [Nonlinear self-scaling conjugate gradient methods for large-scale optimization problems, Ph.D. thesis, Sun Yat-Sen University (2007)], we propose two modified methods of the new formula. The two modified methods all can generate sufficient descent directions which is independent of the line search used. Under some mild conditions, the global convergence and the linearly convergent rate of the two modified methods are established. The numerical results show that the proposed methods are efficient.

MSC:

90C30 Nonlinear programming
65K05 Numerical mathematical programming methods

Citations:

Zbl 1106.65056
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References:

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