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求解界约束优化的一种新的非单调谱投影梯度法

毕亚倩, 刘新为   

  1. 河北工业大学理学院, 天津 300401
  • 收稿日期:2013-04-22 出版日期:2013-11-15 发布日期:2013-12-03
  • 基金资助:

    国家自然科学基金资助项目(11271107)。

毕亚倩, 刘新为. 求解界约束优化的一种新的非单调谱投影梯度法[J]. 计算数学, 2013, 35(4): 419-430.

Bi Yaqian, Liu Xinwei. A NEW NONMONOTONE SPECTRAL PROJECTED GRADIENT METHOD FOR BOUND CONSTRAINED OPTIMIZATION[J]. Mathematica Numerica Sinica, 2013, 35(4): 419-430.

A NEW NONMONOTONE SPECTRAL PROJECTED GRADIENT METHOD FOR BOUND CONSTRAINED OPTIMIZATION

Bi Yaqian, Liu Xinwei   

  1. School of Science, Hebei University of Technology, Tianjin 300401, China
  • Received:2013-04-22 Online:2013-11-15 Published:2013-12-03
本文给出求解界约束优化问题的一种新的非单调谱投影梯度算法. 该算法是将谱投影梯度算法与Zhang and Hager [SIAM Journal on Optimization,2004,4(4):1043-1056]提出的非单调线搜索结合得到的方法. 在合理的假设条件下,证明了算法的全局收敛性.数值实验结果表明,与已有的界约束优化问题的谱投影梯度法比较,利用本文给出的算法求解界约束优化问题是有竞争力的.
A new nonmonotone spectral projected gradient method for bound constrained optimization problems is presented. The method is developed by combining the spectral projected gradient method with a nonmonotone line search technique which is presented by Zhang and Hager [SIAM Journal on Optimization, 2004, 14(4): 1043-1056]. Under mild conditions, the method is proved to be globally convergent. Compared with the existing spectral projected gradient methods, our numerical tests show that the presented method here is more competitive.

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[1] Moré J, Toraldo G. On the solution of large scale quadratic programming problem with bound constraints[J]. SIAM Journal on Optimization, 1991, 1: 93-113.

[2] Friedlander A, Martinez J M, Santos S A. A new trust region algorithm for bound constrained minimization[J]. Applied Mathematics and Optimization, 1994, 30: 235-266.

[3] Conn A R, Gould N I M, Toint Ph L. Trust Region Methods. MPS/SIAM Series on Optimization, Society for Industrial and Applied Mathematics (SIAM) , Philadelphia, PA, 2000.

[4] Ulbrich M. Nonmonotone trust region methods for bound-constrained semi-smooth equation with application to nonlinear complementarity problems[J]. SIAM Journal on Optimization, 2001, 11: 889-917.

[5] Birgin E G, Martinez J M, Raydan M. Nonmonotone spectral projected gradient methods on convex sets[J]. SIAM J Optim, 2000, 10: 1196-1211.

[6] Dai Y H, Fletcher R. Projected Barzilai-Borwein methods for large-scale box-constrained quadratic programming[J]. Numer Math, 2005, 100: 21-47.

[7] 周斌, 高立, 戴虹. 求解大规模带边界约束二次规划问题的单调投影梯度法[J]. 中国科学: 数学, 2006, 36 (5): 556-570.

[8] Yu Z S. Solving bound constrained optimization via a new nonmonotone spectral projected gradiet method[J]. Appl. Numer. Math. 2008, 58: 1340-1348.

[9] Yu Z, Sun J, Qin Y. A multivariate spectral projected gradient method for bound constrained optimization[J]. J. Comput. Appl. Math. 2011, 235: 2263-2269.

[10] 王晓. 求解一般界约束优化问题的积极集信赖域方法[J]. 中国科学: 数学, 2011, 41 (4): 377-391.

[11] 鲍吉锋, 朱德通. 有界约束非线性优化问题的仿射共轭梯度路径法[J]. 计算数学, 2009 (01) .

[12] Barzilai J, Borwein J M. Two-point step size gradient methods[M]. IMA J Numer Anal, 1988, 8: 141-148.

[13] Fletcher R. Low Storage Methods for Unconstrained Optimization[M]. Lectures in Applied Mathematics, 1990, 26: 165-179.

[14] Raydan M. On the Barzilai and Borwein choice of steplength for the gradient method[J]. IMA J Numer Anal, 1993, 13: 321-326.

[15] Dai Y H, Liao L Z. R-linear convergence of the Barzilai and Borwein gradient mehtod[J]. IMA J Numer Anal, 2002, 22: 1-10.

[16] Dai Y H, Fletcher R. On the Asymptotic Behaviour of Some New Gradient Method[J]. Mathematical Programming (Series A), 2005, 13(3): 541-559.

[17] Goldstein A A. Convex programming in Hilbert space[J]. Bull Amer Math Soc, 1964, 70: 709-710.

[18] Levitin E S, Polyak B T. Constrained minimization problems[J]. USSR Comput Math Phy, 1996, 6: 1-50.

[19] Grippo L, Lampariello F, Lucidi S. A nonmonotone line search technique for Newton’s method[J]. SIAM J Numer Anal, 1986, 23: 707-716.

[20] Raydan M. The Barzilai and Borwein method for the large scale unconstrained minimization problem[J]. SIAM J Optim, 1997, 7: 26-33.

[21] Zhang H C, HagerWW. A nonmonotone line search technique and its application to unconstrained optimization[J]. SIAM Journal on Optimization, 2004, 14(4): 1043-1056.

[22] 袁亚湘, 孙文瑜. 最优化理论方法[M]. 北京: 科学出版社, 1997.

[23] Bertsekas D P. Nonlinear Programming[M]. Belmont: Athena Scientific, 1995.

[24] Conn A R, Gould N I M and Toint PH L. Testing a class of methods for solving minimization problems with simple bounds on the variable[J]. Mathematics of Computation, 1988, 50: 399-430.
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