半(p,r)-不变凸多目标分式规划的Wolfe型对偶

Wolfe Duality for Multiobjective Fractional Programming with Semi(p,r)-Invexity Functions

半(p,r)-不变凸函数是一类新的广义凸函数,它既是半预不变凸函数,又是(p,r)-预不变凸函数的真推广,从而是熟知的凸函数和不变凸函数的推广形式.首先,利用了一个广义Lagrange向量函数L(x,u),建立了多目标分式规划问题的Wolfe型对偶(FD).接着,在半(p,r)-不变凸性条件下,得到了几个弱对偶、强对偶和严格逆对偶定理.其结论具有一般性,推广了许多涉及凸函数、不变凸函数、半预不变凸函数和(p,r)-(预)不变凸函数的文献的结论.

Semi（p,r）-invexity functions are new generalized invex functions.They are real generalization of the semi preinvexity functions and（p,r）-preinvexity functions,thus they are the generalization of well known convexity functions and invexity functions.First,by using a generalized Lagrange vector function L（x,u）,the Wolfe dual（FD） of the multiobjective fractional programming problems is established.Second,some weak,strong and strict converse duality theorems are derived under semi（p,r）-invexity assumptions.The work generalizes many results on programming problems with convex functions,invex functions,semipreinvexity functions and（p,r）-（pre）invexity functions.