摘要
B-(p,r)-不变凸函数是一类新的广义凸函数,它既是不变B-凸函数,又是(p,r)-不变凸函数的推广形式.首先,利用B-(p,r)-不变凸函数讨论了目标函数和约束函数均可微的多目标分式规划问题(FP),得到了目标函数和约束函数在B-(p,r)-不变凸函数限制下可行解为有效解的一个最优性充分条件;其次,利用B-(p,r)-不变凸函数建立了多目标分式规划问题(FP)的W olfe型对偶,证明了目标函数和约束函数在B-(p,r)-不变凸函数限制下的弱对偶,强对偶和严格逆对偶定理.其结论具有一般性,推广了许多涉及不变凸,不变B-凸,(p,r)-不变凸和B-(p,r)-不变凸函数的文献的结论.
B-（p,r）-invexity functions are new generalized invex functions. They are generalization of the B-invexity functions and （p ,r）-invexity funcions. First, by using B-（p ,r） -invexity functions ,the multiobjective fractional programming problems （FP） are con- sidered, in which the objective and the constraint functions are differentiable. The sufficient optimality condition for an efficient solution to exist is established, under B-（p,r）-invexity assumptions on objective and the constraint functions. Second, by using B-（p,r）-invexity functions, the Wolfe dual of the programming problems （FP） is considered, in which the objective and the constraint functions are differentiable. The weak, strong and strict converse duality theorems are proved, under B-（p,r）-invexity assumptions on objective and constraint functions. The work generalizes many results on programming problems with invex functions, B-invexity functions, （p, r） -invexity functions and B- （p, r ） - invexity functions.
出处
《四川师范大学学报（自然科学版）》
CAS
CSCD
北大核心
2008年第1期88-92,共5页
Journal of Sichuan Normal University（Natural Science）
基金
国家自然科学基金(10171118)
重庆市教委科学技术研究基金资助项目
