B-(p,r)-预不变凸规划的Wolfe对偶问题与极小化问题  

Wolfe Duality and Minimize Problem with B-(p,r)-pre-invex Programming

作　　者：彭再云[1] 万轩[1,2] 

机构地区：[1]重庆交通大学理学院,重庆400074 [2]重庆师范大学数学学院,重庆401331

出　　处：《重庆师范大学学报（自然科学版）》2010年第6期1-6,共6页Journal of Chongqing Normal University:Natural Science

基　　金：重庆市科委研究项目(No.CSTC2008BB0346);重庆市教委资助课题(No.KJ100405,No.KJ070404);重庆市高教研究项目(No.0833141)

摘　　要：B-(p,r)-预不变凸函数是一类新的广义凸函数,它是B-(p,r)-不变凸函数的推广。本文讨论了B-(p,r)-预不变凸函数的一些性质;然后利用B-(p,r)-预不变凸型函数建立了目标函数和约束函数均可微的多目标规划问题的W olfe型对偶,证明了目标函数和约束函数在B-(p,r)-预不变凸型函数条件下的弱对偶,强对偶和严格逆对偶定理;最后给出了B-(p,r)-预不变凸函数在关于目标函数的极小化问题中的两个重要应用,即建立目标函数在B-(p,r)-预不变凸函数条件下的极小化问题(P),证明了它的局部最优解是全局最优解,它的解集是p-不变凸集,且得出如果问题(P)存在最优解,则最优解唯一。本文结论具有一般性,推广了涉及预不变凸函数、B-预不变凸函数和(p,r)-预不变凸函数文献的一些结论。B-（p,r）-pre-invex functions is a generalized convex functions.It＇s a generalization of the B-（p,r）-invex functions.In this paper,firstly,some properties of the B-（p,r）-pre-invex functions are discussed.Secondly,by using the B-（p,r）-pre-invex functions,Wolfe duality of the multi-objective programming problems is considered,in which the objective and the constraint functions are differentiable.The weak,strong and strict converse duality results are established.Finally,we give two important applications about minimize problem which objective function is B-（p,r）-pre-invex functions.The minimize problem is established under B-（p,r）-pre-invexity assumption on objective function.We obtain that a local optimum of this minimize problem is also a global optimum,and the optimal set is p-invex set.If optimum solution exists on minimize problem（P）,it must be unique.The work generalizes some results on programming problems with pre-invex functions,B-pre-invex functions and（p,r）-pre-invex functions.

关 键 词：B-(p r)-预不变凸函数 多目标规划 WOLFE型对偶 极小化问题 

分 类 号：O221.1[理学—运筹学与控制论]