一类非光滑规划问题的Mond Weir和Wolf对偶  

Mond Weir Dual and Wolf Dual in a Class of Nonsmooth Programming Problems

作　　者：赵克全[1] 罗杰[1] 唐莉萍[1] 

机构地区：[1]重庆师范大学数学与计算机科学学院,重庆400047

出　　处：《重庆师范大学学报（自然科学版）》2010年第1期7-10,25,共5页Journal of Chongqing Normal University:Natural Science

基　　金：重庆师范大学青年基金(No.08XLQ01)

摘　　要：本文考虑带等式和不等式约束的非光滑B-(p,r)单目标规划的对偶问题,研究了函数λf+∑im=1μigi+∑jp=1vjhj为严格B-(p,r)不变凸性条件下Mond Weri对偶模型的弱对偶、强对偶、逆对偶和严格逆对偶,函数f+∑im=1μigi+∑jp=1vjhj为B-(p,r)不变凸性条件下Wolf对偶模型的弱对偶和强对偶以及严格B-(p,r)不变凸性条件下限制逆对偶和严格逆对偶。在无约束规格的条件下证明了该类非光滑规划问题的Mond Weir和Wolf对偶模型相应的对偶性结果。本文的结果是对最近一些文献中相应结果的改进与完善。In this paper duality in a class of nonsinooth B-（p, r）programming problem with equality and inequality constraints is considered. Weak duality, strong duality, converse duality and strict converse duality are researched in Mond Weir dual under strict B-（p,r） invexity of λf＋∑mi=1μigi＋∑pj=1vjhj. Weak duality and strong duality are researched in Wolf dual under B-（p,r） invexity P of f＋∑mi=1μigi＋∑pj=1vjhj and restricted converse duality and strict converse duality are researched under strict B-（p,r） invexity.Some conrresponding duality theorems are proved without any constraints. Our results generalize and improve some known results.

关 键 词：B-(p r)不变凸性 MOND Weir对偶 Wolf对偶 非光滑规划 

分 类 号：O221.2[理学—运筹学与控制论] O172.2[理学—数学]