A two-term PRP-based descent method. (English) Zbl 1138.90028

Summary: In this paper, by the use of the project of the PRP (Polak-Ribiére-Polyak) conjugate gradient direction, we develop a PRP-based descent method for solving unconstrained optimization problems. The method provides a sufficient descent direction for the objective function. Moreover, if exact line search is used, the method reduces to the standard PRP method. Under suitable conditions, we show that the method with some backtracking line search or the generalized Wolfe-type line search is globally convergent. We also report some numerical results and compare the performance of the method with some existing conjugate gradient methods. The results show that the proposed method is efficient.


90C30 Nonlinear programming
65K05 Numerical mathematical programming methods
Full Text: DOI


[1] DOI: 10.1145/200979.201043 · Zbl 0886.65058
[2] DOI: 10.1007/s101070100263 · Zbl 1049.90004
[3] Dai Y.H., Nonlinear Conjugate Gradient Methods (2000)
[4] DOI: 10.1137/0802003 · Zbl 0767.90082
[5] Grippo L., Math. Program. 78 pp 375– (1997)
[6] DOI: 10.1137/030601880 · Zbl 1093.90085
[7] Hager W.W., Pacific J. Optim. 2 pp 35– (2006)
[8] DOI: 10.1145/1132973.1132979 · Zbl 1346.90816
[9] DOI: 10.1007/BF01589116 · Zbl 0696.90048
[10] DOI: 10.1007/BF00940464 · Zbl 0702.90077
[11] Polak E., Rev. Francaise Imformat Recherche Opertionelle 16 pp 35– (1969)
[12] DOI: 10.1016/0041-5553(69)90035-4 · Zbl 0229.49023
[13] DOI: 10.1137/1028154 · Zbl 0624.90091
[14] DOI: 10.1093/imanum/drl016 · Zbl 1106.65056
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