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Hilbert空间中的不可微最优化问题的基路径增量目标水平算法 被引量：1

Path-Based Incremental Target Level Algorithm for Nondifferentiable Optimization in a Hilbert Space
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摘要 主要研究了Hilbert空间中的一类不可微最优化问题的基路径增量目标水平算法.证明了当约束集合为有界集时,问题的最优解集非空,且这时通过算法生成的迭代点列是弱收敛于最优解的.. In this paper, we consider path-based incremental target level algorithm a type of nondifferentiable optimization in a Hilbert space. We prove that the problem has solu- tions when the constraint set is bounded, and the sequence generated in this way is weakly convergent.
作者 张鹏
机构地区 牡丹江师范学院理学院
出处 《数学的实践与认识》 CSCD 北大核心 2014年第12期284-290,共7页 Mathematics in Practice and Theory
基金 牡丹江师范学院青年一般项目(QY201318) 黑龙江省教育厅科技面上项目(12531726)
关键词 HILBERT空间 基路径增量目标水平算法 不可微最优化问题 Hilbert space path-based incremental target level algorithm nondifferentiable optimization
分类号 O177.1 [理学—基础数学]
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参考文献8

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同被引文献7

  • 1Hestenes M R, Stiefel E. Methods of conjugate gradients for solving linear systems[J]. Journal of Research of the National Bureau of Standards, 1952,49(6) : 409-439.
  • 2Fletcher R, Reeves C. Function minimization by conjugate gradients[J]. Computer Journal, 1964,7(2).. 149-154.
  • 3Kiwiel K C. The Efficiency of Subgradient Projection Methods for Convex Optimization. Part I General Level Methods[J]. SIAM. Journal on Control and Optimization, 1996,34(2) 660-676.
  • 4Nedic A, Bertsekas D P. Incremental Subgradient Methods for Nondifferentiable Optimization[J]. SIAM. Journal on Optimization, 2001,12(1) : 109-138.
  • 5Fukushima M, Mine H. A generalized proximal point algorithm for certain nonconvex minimization problems[J]. International Jour- nal of Systems Science, 1981,12 : 989-1000.
  • 6Tseng P, Yun S. A coordinate gradient descent method for nonsmooth separable minimization[J]. Mathematieal Programming, 2009, 117: 387-423.
  • 7He B S, Yuan X M. An accelerated inexact proximal point algorithm for convex minimization[J]Journal of Optimization Theory and Applications, 2012,154(2) : 536-548.

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数学的实践与认识
2014年 第12期

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