B-(p,r)-预不变凸规划的Mond-Weir对偶问题研究  

The Research of Mond-weir Duality for Programming with B-(p,r)-pre-invexity Function

作　　者：万轩[1,2] 彭再云[2] 

机构地区：[1]重庆师范大学数学学院,重庆401311 [2]重庆交通大学理学院,重庆400074

出　　处：《重庆师范大学学报（自然科学版）》2011年第1期1-6,17,共7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);重庆市高等教育教学改革资助项目(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,本文对其性质及B-(p,r)-预不变凸多目标规划问题的Mond-Weir型对偶进行了研究。首先,给出了B-(p,r)-预不变凸函数的几个基本性质,表明B-(p,r)-预不变凸函数仍然满足加法,数乘和复合函数运算性质,并举例说明了B-(p,r)-预不变凸函数是B-(p,r)-不变凸函数的真推广。然后,重点讨论了B-(p,r)-预不变凸多目标规划问题及其Mond-Weir型对偶问题的解的情况。分别给出了关于目标函数和约束函数均可微的多目标规划问题(VP)在B-(p,r)-预不变凸型条件下的弱对偶、强对偶和严格逆对偶定理。其结论具有一般性,推广了涉及预不变凸函数、B-预不变凸函数和(p,r)-预不变凸函数的文献的相关结论。B-（p,r）-pre-invex function is a new generalized convex function and it＇s a generalization of B-（p,r）-invex functions.In this paper,the property of the B-（p,r）-pre-invex function and its Mond-weir duality of the multi-objective programming problems are considered.First,some basic properties of the B-（p,r）-pre-invex function are introduced to show that the properties of addition,multiplication and composition to the B-（p,r）-pre-invex function are still satisfying,meanwhile,some examples are given to illustrate that the B-（p,r）-pre-invex function is a ture generalization of B-（p,r）-invex function.Second,the multi-objective programming problems of B-（p,r）-pre-invex function and the solution for its Mond-weir duality problems are emphasized here.By using the B-（p,r）-pre-invex function,the weak,strong and strict converse duality results are established for multi-objective problems（VP） which concerns about objective function and constraint function.The results extend the corresponding ones in the literature on programming problems with pre-invex function,B-pre-invex function and（p,r）-pre-invex function.

关 键 词：B-(p r)-预不变凸函数 多目标规划 MOND-WEIR型对偶 

分 类 号：O221.1[理学—运筹学与控制论]