B-(p,r)-不变凸规划问题的最优性讨论

Optimality Discussions for Programming Problems with B-(p,r)-Invexity Functions

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,从而是熟知的凸函数和不变凸函数的推广形式.这篇文章利用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规划问题,证明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几个最优性充分条件,其结论具有一般性,推广了许多涉及不变凸函数、不变B-凸函数和(p,r)-不变凸函数的文献的结论.

B-(p,r)-invexity functions are new generalized invex functions. It is generalization of the B-invexity functions and (p,r)-invexity functions, thus it is the generalization of well known invex functions and invexity functions. By using B-(p,r)-invexity functions, the multiobjective programming problems are considered, in which the objective and the constraint functions are differentiable. The sufficient optimality conditions for an efficient solution are established, under B-(p,r)-invexity assumptions on objective and the constraint functions. The work generalizes many results on programming problems with invex functions, B-invexity functions and (p,r)-invexity functions.