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复合凸优化问题全对偶性的等价刻画 被引量：6

Some Characterizations of Total Duality for a Composed Convex Optimization
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摘要 先建立一类复合凸优化问题的对偶问题,再利用次微分性质引入关于复合凸函数的一类新的Moreau-Rockafellar法则,等价刻画了该复合凸优化问题的稳定全对偶及全对偶. We first introduced the dual schemes for a composed convex optimization problem.Then,using the properties of subdifferential,we introduced a new Moreau-Rockafellar formula for a composed convex function.And using the Moreau-Rockafellar formula,we obtained some necessary and sufficient conditions which characterize the stable total duality for the composed convex optimization problem.
作者 孙祥凯
机构地区 重庆工商大学数学与统计学院 重庆大学自动化学院
出处 《吉林大学学报（理学版）》 CAS CSCD 北大核心 2015年第1期33-36,共4页 Journal of Jilin University:Science Edition
基金 国家自然科学基金(批准号:11301570) 中国博士后科学基金(批准号:2013M540697) 重庆市基础与前沿研究计划项目(批准号:cstc2013jcyjA00003)
关键词 复合凸优化问题 Moreau-Rockafellar法则 稳定全对偶 全对偶 composed convex optimization problem Moreau-Rockafellar formula stable total duality total duality
分类号 O221.6 [理学—运筹学与控制论] O224 [理学—运筹学与控制论]
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参考文献8

  • 1Bot R I, Grad S M, Wanka G. A New Constraint Qualification for the Formula of the Subdifferential of Composed Convex Functions in Infinite Dimensional Spaces [J]. Mathematische Nachrichten, 2008, 281(8): 1088 -1107.
  • 2Bot R I, Grad S M, Wanka G. Generalized Moreau-Rockafellar Results for Composed Convex Functions [J]. Optimization, 2009, 58(7): 917- 933.
  • 3赵丹,孙祥凯.复合凸优化问题的稳定强对偶[J].吉林大学学报（理学版）,2013,51(3):441-443. 被引量：6
  • 4LI Chong, FANG Donghui, L6pez G, et al. Stable and Total Fenchel Duality for Convex Optimization Problems in Locally Convex Spaces [J]. SIAM Journal on Optimization, 2009, 20(2) ： 1032- 1051.
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  • 6got R 1. Coniugate Duality in Convex Optimization[M]. Berlin: Springer Verlag, 2010.
  • 7FANG Donghui, LI Chong, YANG Xiaoqi. Stable and Total Fenchel Duality for DC Optimization Problems in Locally Convex Spaces [J]. SIAM Journal on Optimization, 2011, 21(3): 750-760.
  • 8FANG Donghui, LI Chong, YANG Xiaoqi. Asymptotic Closure Condition and Fenchel I)uality for I)(" Optimization Problems in Locally Convex Spaces[J] Nonlinear Analysis: Theory, Methods :- Applications, 2012, 75(8): 3672-3681.

二级参考文献11

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共引文献5

同被引文献30

  • 1Li C, Fang D H, Lopez C~ et al. Stable and total Fenchel duality for convex optimization problems in locally convex spaces [J]. SIAM J Optim, 2009, 20:1 032-1 051.
  • 2Li C, Ng K F, Pong T K. Constraint qualifications for convex inequality systems with applications in constrained optimization [J]. SI.AM J Optim, 2008, 19: i63-187.
  • 3Fang D H, Li C, Ng K F. Constraint qualifications for optimality conditions and total Lagrangian dualities in convex infinite programming [J]. SIAM J Optim, 2010, 73:1 143-1 159.
  • 4Fang D H, Li C, Ng K F. Constraint qualifications for extended Farkas's lemmas and Lagrangian dualities in convex infinite programming [J]. SIAM J Optim, 2009, 20: 131-132.
  • 5Li C, Ng K F, Pong T K. The SECQ linear regularity and the strong CHIP for infinite system of closed convex sets in normed linear spaces [J]. SIAM J Optim, 2007, 15: 643-666.
  • 6Gobema M A, Jeyakumar V, Lopez M A. Necessary and sufficient conditions for solvability of systems of infinite convex inequalities [J]. Nonlinear Anal, 2008, 68:1 184-1 194.
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  • 8Zhou Y Y, Li G~ The Totand-Fenchel-Lagrange duality of DC programs for composite convex functions[J]. Numerical Algebra Control and Optimization, 2014, 4: 9-23.
  • 9Zalinescu C. Convex Analysis in General Vector Spaces [M]. New Jersey: World Scientific, 2002.
  • 10Rockafellar R T. Convex Analysis [M]. Princeton: Princeton University Press, 1970.

引证文献6

二级引证文献4

吉林大学学报（理学版）
2015年 第1期

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