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一个新的MBFGS信赖域算法 被引量：1

A NEW MBFGS OF TRUST REGION ALGORITHM
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摘要 本文研究了无约束最优化问题.利用MBFGS信赖域算法的基本思想,通过对BFGS校正公式的改进,并结合线搜索技术,提出了一种新的MBFGS信赖域算法,拓宽了信赖域算法的适用范围,并在一定条件下证明了该算法的全局收敛性和超线性收敛性. In this paper, we study unconstrained optimization problems. By using the basic idea of the MBFGS trust region algorithm, we improve BFGS correction formula, combine with line search technique and put forward a new MBFGS trust region algorithm which broadens the scope of application of the trust region algorithm. Under certain conditions, the global convergence and superlinear convergence of the algorithm is proved.
作者 景书杰 苗荣 李少娟
机构地区 河南理工大学数学与信息科学学院 河南护理职业学院
出处 《数学杂志》 CSCD 北大核心 2014年第3期569-576,共8页 Journal of Mathematics
基金 国家自然科学基金项目(10671057) 河南理工大学运筹学与控制论重点学科资助项目(10671057)
关键词 无约束最优化 信赖域算法 BFGS(MBFGS)方法 线搜索 unconstrained optimization trust region BFGS（MBFGS） modification linesearch
分类号 O224 [理学—运筹学与控制论]
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参考文献10

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同被引文献11

  • 1马昌风.最优化方法及其Matlab程序设计[M].北京:科学出版社,2010:87-96.
  • 2Mishali M, Elder Y C. From theory to practice: sub-nyquist sampling of sparse wideband analog signals[J]. IEEE J. Selected Topics Sign. Proc., 2009, 4(2): 375-391.
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  • 4Zhu Hong, Xiao Yunhai, Wu Soon- Vi. Large sparse signal recovery by conjugate gradient algorithm based on smoothing technique[J]. Comput. Math. Appl., 2013, 66: 24-32.
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  • 6Candes E, Romberg J. Quantitative robust uncertainty principles and optimally sparse decompositions[J]. Found. Comput. Math., 2006, 6: 227-254.
  • 7Candes E, Tao T. Near optimal signal recovery from random projections: universal encoding strategies[J]. IEEE Trans. Info. Theory, 2006, 52: 5406-5425.
  • 8Donoho L D. Compressed sensing[J]. IEEE Trans. Inform. Theory, 2006, 52: 1289-1306.
  • 9Aybat S N, Iyengar G. A first-order smoothed penalty method for compressed sensing[J]. SIAM J. Optim., 2011, 21(1): 287-313.
  • 10Nesterov Y. Smooth minimization of non-smooth functions[J]. Math. Prog., 2005, 103: 127-152.

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数学杂志
2014年 第3期

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