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指数型增广拉格朗日函数在广义半无限规划中的应用 被引量：1

ON THE USE OF EXPONENTIAL-TYPEAUGMENTED LAGRANGIAN FUNCTION INGENERALIZED SEMI-INFINITE MIN-MAXPROGRAMMING
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摘要 本文利用指数型增广拉格朗日函数将一类广义半无限极大极小问题在一定条件下转化为标准的半无限极大极小问题,使它们具有相同的局部与全局最优解.我们给出了两个转化条件:一个是充分与必要条件,另一个是在实际中易于验证的充分条件.通过这种转化,我们给出了广义半无限极大极小问题的一个新的一阶最优性条件. Under certain conditions, we ues the exponential-type augmented Lagrangian function to transform a class of gen- eralized semi-infinite min-max problems into common semi-infinte rain-max problems, with the same set of local and global solutions. We give two conditions for the transformation. One is a necessary and sufficient condition, the other is a sufficient condition which can be verified easily in practice. From the transformation, we obtain a new first-order optimality condition for this class of generalized semi-infinite min-max problems.
作者 刘芳 王长钰
机构地区 曲阜师范大学运筹与管理学院
出处 《经济数学》 2007年第4期420-426,共7页 Journal of Quantitative Economics
基金 国家自然科学基金资助项目(10571106 10701047)
关键词 标准半无限规划 广义半无限极大极小规划 增广拉格朗日函数 一阶了优性条件 Common semi-infinite programming, generalized semi-infinite rain-max programming, Augmented Lagrangian functions, First-order optimality conditions.
分类号 O211.2 [理学—概率论与数理统计]
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参考文献9

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  • 2Polak E., Optimization: Algorithms and Consistent Approximations. New York, NY: Springer Verlag, 1997.
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同被引文献11

  • 1杜学武,张连生,尚有林,李铭明.带有不等式约束的非线性规划问题的一个精确增广Lagrange函数[J].应用数学和力学,2005,26(12):1493-1499. 被引量：6
  • 2Marin S P.Optimal parameterization of curves for robot trajectory design[J].IEEE Transactions on Automatic Control,1988,33(2):209-214.
  • 3Wang D,Fang S C.A semi-infinite programming model for earliness/Tardiness production planning with a genetic algorithm[J].Computers and Mathematics with Applications,1996,31(8):95-106.
  • 4Hettich R,Kortanek K O.Semi-infinite programming:theory,methods and applications[J].SIAM Review,1993,35 (3):380-429.
  • 5Lopez M,Still G.Semi-infinite programming[J].European Journal of Operational Research,2007,180:491-518.
  • 6Still G.Discretization in semi-infinite programming:the rate of convergence[J].Mathematical Programming,2001,91 (1):53-69.
  • 7Goberna Mát,López M A.Semi-infinite programming recent advances[M].Dordrecht,Boston,London:Kluwer Academic Publishers,2001.
  • 8Polak E.Optimization:algorithms and consistent approximations[M].Berlin,Heidelberg:Springer-Verlag,1997.
  • 9Polak E,Royset J O.Algorithms for finite and semi-infinite min-max-min problems using adaptive smoothing techniques[J].Journal of Optimization Theory and Application,2003,119 (3):421-457.
  • 10Royset J O,Polak E,Der Kiureghian.Adaptive approximations and exact penalization for the solution of generalized semi-infinite min-max problems[J].SIAM Journal on Optimization,2003,14(1):1-34.

引证文献1

经济数学
2007年 第4期

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