非光滑半无限多目标规划的最优性及混合对偶  

Optimality Condition and Duality for Nonsmooth Multiobjective Semi-infinite Programming Problems

作　　者：万轩[1] 赵克全[1] 

机构地区：[1]重庆师范大学数学学院,重庆400047

出　　处：《重庆师范大学学报（自然科学版）》2012年第2期7-11,共5页Journal of Chongqing Normal University:Natural Science

基　　金：重庆市自然科学基金项目(No.2011BA0030);重庆市科委运筹学与系统工程重点实验室项目(No.CSTC2011KLORSE02);重庆市教委科技项目(No.KJ110625)

摘　　要：本文研究了非光滑半无限多目标规划(NSIMP)的最优性条件及混合型对偶。首先,在Fritz-John必要条件的基础上建立了Karush-Kuhn-Tucker必要条件,即设为(NSIMP)的有效解和gj,j∈()为关于η的严格不变凸函数,则存在0,μj≥0,j∈J且ūj≠0对有限多个j∈J,使得(4)-(6)成立。然后建立了Karush-Kuhn-Tucker充分条件,即设x为(NSIMP)的可行解,在x处满足Karush-Kuhn-Tucker条件(4)-(6)式,fi,i∈I是关于η的不变凸函数,gj,j∈J()是关于相同η的严格不变凸函数,则为(NSIMP)的有效解。最后在不变凸性条件下,证明了混合对偶模型的弱对偶,强对偶和逆对偶定理。本文的主要结果推广并改进了一些已有的结论。In this paper, we investigated the optimality condition and mixed duality for nonsmooth semi-infinite muhiobjective program （NSIMP）. Firstly, we proved Karush-Kuhn-Tucker necessary on the basis of the Fritz-John necessary condition, i. e. , let x^- be an effi- cient solution of the problem （NS1MP） and gi ,J e （x^-） are strictly invex with respect to η. Then there exist Aλ^-0 ,μj ≥0, Aj ∈ J, and for finitely many j ∈ J such that （4） - （ 6 ） hold. Furthermore, we proved Karush-Kuhn-Tucker sufficient conditions, i.e. , let x^- be feasible in （NSIMP）, Karush-Kuhn-Tucker conditions （4） - （6） are satisfied at x^-, fl, i e I are invex with respect to η, g/,J e J（x^-） are strictly invex with respect to the same η. Then x^- is an efficient solution of the problem （NSIMP）. Finally, weak dual theorem, strong dual theorem and converse dual theorem for nonsmooth semi-infinite program involving in vexity are established. Our results im- prove and generalize some known results.

关 键 词：非光滑半无限多目标规划 最优性条件 混合型对偶 

分 类 号：O221.2[理学—运筹学与控制论]