期刊文献+
任意字段
题名或关键词
题名
关键词
文摘
作者
第一作者
机构
刊名
分类号
参考文献
作者简介
基金资助
栏目信息

一类广义半无限规划问题的一阶最优性条件

First-order Optimality Condition on a Kind of Generalized Semi-infinite Programming Problem
下载PDF
导出
摘要 本文利用一个精确增广Lagrange函数研究了一类广义半无限极小极大规划问题。在一定的条件下将其转化为标准的半无限极小极大规划问题。研究了这两类问题的最优解和最优值之间的关系,利用这种关系和标准半无限极小极大规划问题的一阶最优性条件给出了这类广义半无限极小极大规划问题的一个新的一阶最优性条件。 In this paper,a kind of generalized semi-infinite min-max programming problem is transformed into a common semi-infinite min-max programming problem by utilizing a exact augmented Lagrange function.The relations of optimal solutions and optimal values between generalized semi-infinite min-max programming problem and common semi-infinite min-max programming problem are discussed.According to these relations and the first-order optimality condition of common semi-infinite min-max programming problem,the first-order optimality condition of this kind of generalized semi-infinite min-max programming problem is presented.
作者 李梅霞
机构地区 潍坊学院数学与信息科学学院
出处 《运筹与管理》 CSSCI CSCD 北大核心 2012年第1期34-39,共6页 Operations Research and Management Science
基金 国家自然科学基金资助项目(10171055 10171118) 山东省自然科学基金资助项目(ZR2009AL019) 山东省高校科研发展计划资助项目(J09LA53)
关键词 运筹学 广义半无限规划 精确增广Lagrange函数 一阶最优性条件 operational research generalized semi-infinite programming exact augmented Lagrange function first-order optimality condition
分类号 O221.2 [理学—运筹学与控制论]
  • 相关文献

参考文献12

  • 1Marin S P.Optimal parameterization of curves for robot trajectory design[J].IEEE Transactions on Automatic Control,1988,33(2):209-214.
  • 2Wang 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.
  • 3Hettich R,Kortanek K O.Semi-infinite programming:theory,methods and applications[J].SIAM Review,1993,35 (3):380-429.
  • 4Lopez M,Still G.Semi-infinite programming[J].European Journal of Operational Research,2007,180:491-518.
  • 5Still G.Discretization in semi-infinite programming:the rate of convergence[J].Mathematical Programming,2001,91 (1):53-69.
  • 6Goberna Mát,López M A.Semi-infinite programming recent advances[M].Dordrecht,Boston,London:Kluwer Academic Publishers,2001.
  • 7Polak E.Optimization:algorithms and consistent approximations[M].Berlin,Heidelberg:Springer-Verlag,1997.
  • 8Polak 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.
  • 9Royset 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.
  • 10Polak E,Royset J O.On the use of augmented Lagranges in the solution of generalized semi-infinite min-max problems[J].Computational Optimization and Application,2005,31:173-192.

二级参考文献23

  • 1Bertsekas D P.Constrained Optimization and Lagrange Multipliers Methods[M].New York:Academic Press,1982.
  • 2Burke J.An exact penalization viewpoint of constrained optimization[J].SIAM J Control Optim,1991,29(4):968-998.
  • 3Di Pillo G.Exact penalty methods[A].In:Spedicato E Ed.Algorithms for Continuous Optimization: the State of the Art[C]. Boston: Kluwer Academic Press,1994,209-253.
  • 4Di Pillo G,Grippo L.Exact penalty functions in constrained optimization[J].SIAM J Control Optim,1989,27(6):1333-1360.
  • 5Yevtushenko Y G,Zhadan V G.Exact auxiliary functions in optimization problems[J].USSR Comput Maths and Math Phys,1990,30(1):31-42.
  • 6Contaldi G,Di Pillo G,Lucidi S.A continuously differentiable exact penalty function for nonlinear programming problems with unbounded feasible set[J].Oper Res Lett,1993,14(3):153-161.
  • 7Di Pillo G,Grippo L.A continuously differentiable exact penalty function for nonlinear programming problems with inequality constraints[J].SIAM J Control Optim,1985,23(1):72-84.
  • 8Di Pillo G,Grippo L.On the exactness of a class of nondifferentiable penalty functions[J].J Optim Theory Appl,1988,57(3):399-410.
  • 9Lucidi S.New results on a continuously differentiable exact penalty function[J].SIAM J Optim,1992,2(4):558-574.
  • 10Di Pillo G, Grippo L. A new augmented Lagrangian function for inequality constraints in nonlinear programming problems[J].J Optim Theory Appl,1982,36(4):495-519.

共引文献5

运筹与管理
2012年 第1期

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部