具有充分下降性的两个共轭梯度法

江羡珍, 简金宝, 马国栋

数学学报 ›› 2014, Vol. 57 ›› Issue (2) : 365-372.

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数学学报 ›› 2014, Vol. 57 ›› Issue (2) : 365-372. DOI: 10.12386/A2014sxxb0036
论文

具有充分下降性的两个共轭梯度法

    江羡珍1, 简金宝1,2, 马国栋1
作者信息 +

Two Conjugate Gradient Methods with Sufficient Descent Property

    Xian Zhen JIANG1, Jin Bao JIAN1,2, Guo Dong MA1
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文章历史 +

摘要

对无约束优化问题，本文给出了两个改进的共轭梯度法公式. 在不依赖于任何线搜索条件下，由新公式所产生的算法方向均是充分下降的，且在标准Wolfe非精确线搜索条件下，算法都具有全局收敛性. 最后，对新算法进行大量的比对试验，数值结果表明所提方法是有效的.

Abstract

In this paper, two improved conjugate gradient methods are proposed for unconstrained optimization. The two presented methods can generate sufficient decent directions at every iteration depending on no line search, moreover, the global convergence of the two proposed methods are proved under the standard Wolfe line search. Some elementary numerical experiments are reported, which show that the two proposed methods are promising.

关键词

无约束优化 / 共轭梯度法 / 充分下降性 / 全局收敛性

Key words

unconstrained optimization / conjugate gradient method / sufficient descent property / global convergence

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江羡珍, 简金宝, 马国栋. 具有充分下降性的两个共轭梯度法. 数学学报, 2014, 57(2): 365-372 https://doi.org/10.12386/A2014sxxb0036
Xian Zhen JIANG, Jin Bao JIAN, Guo Dong MA. Two Conjugate Gradient Methods with Sufficient Descent Property. Acta Mathematica Sinica, Chinese Series, 2014, 57(2): 365-372 https://doi.org/10.12386/A2014sxxb0036

参考文献

[1] Dai Y. H., A nonmonotone conjugate gradient algorithm for unconstrained optimization, J. Syst. Sci. Complex., 2002, 15: 139-145.

[2] Dai Y. H., Yuan Y. X., A nonlinear conjugate gradient method with a strong global convergence property, SIAM J. Optim., 1999, 10: 177-182.

[3] Dai Y. H., Yuan Y. X., An efficient hybrid conjugate gradient method for unconstrained optimization, Ann. Oper. Res., 2001, 103: 33-47.

[4] Dai Y. H., Yuan Y. X., Nonlinear Conjugate Gradient Methods (in Chinese), Shanghai Scientific and Technical Publishers, Shanghai, 2000.

[5] Dai Z. F., Wen F. H., Another improved Wei-Yao-Liu nonlinear conjugate gradient method with sufficient descent property, Appl. Math. Comput., 2012, 218: 7421-7430.

[6] Dolan E. D., Morè J. J., Benchmarking optimization software with performance profiles, Math. Program., 2002, 91: 201-213.

[7] Fletcher R., Reeves C., Function minimization by conjugate gradients, Comput. J., 1964, 7: 149-154.

[8] Glibert J. C., Nocedal J., Global covergence properties of conjugate gradient method for optimization, SIAM J. Optim., 1992, 2: 21-42.

[9] Hager W. W., Zhang H., A new conjugate gradient method with guaranteed descent and an efficient line search, SIAM J. Optim., 2005, 16: 170-192.

[10] Hestenes M. R., Stiefel E. L., Method of conjugate gradient for solving linear systems, J. Res. Natl. Bur. Stand, 1952, 49: 409-436.

[11] Jiang X. Z., Jian J. B., A sufficient decent Dai-Yuan type nonlinear conjugate gradient method for unconstrained optimization problems, Nonlinear Dyn., 2013, 72(1-2): 101-112.

[12] Jiang X. Z., Han L., Jian J. B., A globally convergent mixed conjugate gradient method with Wolfe line search (in Chinese), Math. Numer. Sin., 2012, 34(1): 103-112.

[13] Moré J. J., Garbow B. S., Hillstrome K. E., Testing unconstrained optimization software, ACM Trans. Math. Softw., 1981, 7: 17-41.

[14] Polyak B. T., The conjugate gradient method in extreme problems, USSR Comput. Math. Math. Phys., 1969, 9: 94-112.

[15] Polak E., Ribére G., Note surla convergence des mèthodes de directions conjugèes, Rev. Fr. Inform. Rech. Oper., 1969, 3(1): 35-43.

[16] Yan H., Chen L. P., A new hybrid conjugate gradient algorithm with sufficient descent property (in Chinese), Acta Math. Appl. Sin., 2011, 34(4): 634-643.

[17] Yao S. W., Wei Z. X., Huang H., A note about WYL's conjugate gradient method and its application, Appl. Math. Comput., 2007, 191: 381-388.

[18] Yuan G. L., Lu X. W., A modified PRP conjugate gradient method, Ann. Oper. Res., 2009, 166: 73-90.

基金

广西自然科学基金资助项目（2013GXNSFAA019009）；广西高校科研资助项目（2013YB196）及广西高校人才小高地建设创新团队资助计划

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