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不等式约束优化问题的一个势函数 被引量:7

A Potential Function for Solving Inequality Constrained Optimiztion Problems
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摘要 基于Carroll(1961)建立的罚函数,本文给出了不等式约束优化问题的一个势函数,并且讨论了该函数的性质,最后证明了在此基础上建立的对偶算法具有Q-线性收敛性。 Based on the penalty function constructed by Carroll (1961), this paper pre- sented a potential function for inequality constrained optimization problems and discuss the properties of the function. Finally the Q-linear convergence of the dual algorithm, which is based on the potential function, is proved.
出处 《数学进展》 CSCD 北大核心 2004年第3期343-350,共8页 Advances in Mathematics(China)
基金 武汉理工大学博士科研基金与校基金
关键词 势函数 不等式约束 Q-线性收敛性 对偶算法 potential function inequlity constraints Q-linear convergence dual algorithm
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参考文献6

  • 1Carroll C W. The created response surface technique for optimizing nonlinear restrained systems [J]. Operations Research, 1961, 9(2): 169-184.
  • 2Bertsekas D B. Constrained Optimization and Lagrange Multiplier Methods [M]. New York: Academic Press, 1982.
  • 3Frisch K R. The logarithmic potential method of convex programming [C]. Technical Report, University Institute of Economics, Oslo, Norway, 1955.
  • 4Fiacco A V, McCormick G P. Nonlinear Programming Sequential Unconstrained Minimization Techniques [M]. New York: Wiley, 1968.
  • 5Polyak R A. Smooth optimization methods for minimax problems [J]. SIAM Journal of Control and Optimization, 1988, 26: 1274-1286.
  • 6Templeman A B, Li Xingsi. A maximum entropy approach to constrained nonlinear programming [J].Engineering Optimization, 1987, 12: 191-205.

同被引文献21

  • 1张宏伟,张立卫.非凸半定规划的增广Lagrangian的微分的计算(英文)[J].运筹学学报,2004,8(3):66-70. 被引量:1
  • 2冯光财,朱建军,陈正阳,戴吾蛟.基于有效约束的附不等式约束平差的一种新算法[J].测绘学报,2007,36(2):119-123. 被引量:23
  • 3Bertsekas, D. Constrained Optimization and Multiplier Methods. New York: Academic Press,1982.
  • 4Polyak R A. Modified barrier function: theory ang methods[J]. Mathematical Programming,1992,54(2):177-222.
  • 5Polyak R A. Log-Sigmoid multipliers method in constrained optimization[ J ]. Annals of Operations Research, 2001,101:427-460.
  • 6寇述舜.凸分析与二次规划[M].天津:天津大学出版社,1994:144-145.
  • 7Bertsekas, D., Constrained Optimization and Lagrange Multiplier Methods, New York: Academic Press, 1982.
  • 8Polyak, R.A., Modified barrier function: theory and mehtods, Mathematical Programming, 1992, 54(2): 177-222.
  • 9Polyak, R.A., Log-Sigmoid multipliers method in constrained optimization, Annals of Operations Research, 2001, 101: 427-460.
  • 10Fiacco, A.V. and McCormick, G.P., Nonlinear Programming: Sequential Unconstrained Minimization Techniques, New York: Wiley, 1968.

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