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一类无约束优化问题的非单调共轭梯度法 被引量:1

A CLASS OF NONMONOTONE CONJUGATE GRADIENT METHODS FOR UNCONSTRAINED OPTIMIZATION
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摘要 主要研究了一类在推广的线搜索条件下的非单调共轭梯度法 ,并在较弱的假设条件下证明了其全局收敛性 . The conjugate gradient methods with an extended line search is studied. Under mild conditions, the global convergence is proved.
出处 《曲阜师范大学学报(自然科学版)》 CAS 2003年第1期11-14,共4页 Journal of Qufu Normal University(Natural Science)
基金 国家自然科学基金项目 ( 10 1710 5 5 )
关键词 无约束优化问题 非单调共轭梯度法 非单调线搜索 全局收敛性 非线性规划 unconstrained optimization nonmonotone conjugate gradient methods nonmonotone line search global convergence
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参考文献4

  • 1[1]Grippo L, Lampariello F, Lucidi S. A nonmonotone line search technique for Newton's Method[J]. SIAM Journal on Numerical Analysis,1986,123:707~716.
  • 2[2]Lucidi S, Roma M. Nonmonotone conjugate gradient methods for optimization. System Modeling and Optimization[A]. Lecture Notes on Control and Information Sciences[C]. Berlin:Springer Verlag, 1995.
  • 3[3]Liu G H, Jing L L, Han L X, Han D. A class of nonmonotone conjugate gradient methods for unconstrained optimization[J]. Journal of Optimization Theory and Applications,1999,101(1):127~140.
  • 4[4]Powell M J D. Some properties of the variable metric method[A]. Numerical Methods for Nonlinear Optimization[C]. London:Academic Press, 1972.1~7.

同被引文献10

  • 1Al-Baali M. Descent Property and global convergence of the Fletcher-Reeves method with inexact line searches [J]. IMA Journal of Numerical Analysis, 1985,5 ( 1 ) : 121 - 124.
  • 2Gilbert J C, Nocedal J. Global convergence properties of conjugate gradient methods for optimization[J]. SIAM J Optimization, 1992,2 : 21-42.
  • 3Dai Y H, Yuan Y X. A Nonlinear conjugate gradient method with a strong Global convergence propertie[J]. SIAM J Optimization, 1999,10 : 177-182.
  • 4Zoutendijk G. Nolinear programming, computational methods I-A]. In: Integer and Nolinear Programming, Abedie, ed, North-Holland, Amsterdam, 1970. 37-86.
  • 5Jorge J More, Burton S Garbow, Kenneth E Hillstrom. Testing unconstrained optimization software[J].ACM Transactions on Mathematical Software, 1981,7 ( 1 -2) : 17-41.
  • 6Grippo L, Lampariello F, Lueidi S. A nonmonotone line search technique for Neton's methods[J].SIAM Journal on Numerical Analysis, 1986,123 : 707-716.
  • 7Lucidi S, Roma M. Nonmonoton conjugate gradient methods for optimization, System Modeling and Optimization[A].Lecture Notes on Control and Information Sciences[C], Belin. Springer Verlag, 1995.
  • 8Liu G H, Jing L L, Han D. A class of nonmonotone conjugate gradient methods for uncostrained optimization[J]. Journal of Optimization Theory and Applications, 1999,101 (1) : 127-140.
  • 9Powelt M J D. Some properties of the variable metric method[A].Numerical Methods for Nonlinear Optimization[C].London : Academic Press, 1972. 1-7.
  • 10王长钰,韩继业,王磊.无约束最优化的Polak-Ribière和Hestenes—Stiefel共轭梯度法的全局收敛性(英文)[J].运筹学学报,2000,4(3):1-7. 被引量:10

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