一类非光滑规划问题的混合对偶  

The Mixed Dual for a Class of Nonsmooth Programming Problems

作　　者：唐莉萍[1] 蒋华[1] 赵克全[1] 杨新民[1] 

机构地区：[1]重庆师范大学数学学院,重庆400047

出　　处：《四川师范大学学报（自然科学版）》2011年第1期34-37,共4页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(10771228)资助项目;重庆师范大学青年基金(08XLQ01)对本文给予了资助

摘　　要：考虑一类带等式和不等式约束的非光滑多目标规划问题(NMOP).在非光滑B-(p,r)-不变凸性条件下,利用Clarke次微分,将建立此类规划问题的Mixed型对偶,讨论其与原问题间的对偶定理.首先,在B-(p,r)-不变凸性和正则条件下给出弱对偶定理;其次,在无约束规格的条件下,弱对偶定理基础上,利用严格B-(p,r)-不变凸性和正则条件,建立强对偶;最后,给出原问题有效解的逆对偶定理.所得结果是对最近一些文献中相应结果的改进与完善.In this paper,a class of nonsmooth multiobjective programming（NMOP） with equality and inequality constraints is considered.The Mixed dual model for this programming is established,and the duality theory between the dual problem and the primal problem is discussed in terms of Clarke subdifferential,under the assumption of the nonsmoooth B-（p,r）-invxity.Firstly,weak dual theorem is presented by using B-（p,r）-invexity and regularity.Then,on the basis of weak dual theorem,strong dual theorem is established on tne condition of the strict B-（p,r）-invxity and regularity without any constraint qualification.Finally,converse dual theorem is given for the efficient solution of primal problem.This work generalizes and improves some known results.

关 键 词：B-(p r)-不变凸性 混合对偶 非光滑规划 

分 类 号：O221.2[理学—运筹学与控制论] O221.6[理学—数学]