一类非光滑分式半无限规划的最优性条件

Optimality conditions for a class of nonsmooth fractional semi-infinite programming

为了丰富非光滑优化的理论,在一致(Fb,ρ)-凸、一致(Fb,ρ)-伪凸和一致(Fb,ρ)-拟凸等一些非光滑广义凸函数的基础上,研究了涉及此类广义凸性的一类非光滑分式半无限规划.利用反证法证明了上述非光滑分式半无限规划的一系列最优性充分条件.

To enrich the theory of nonsmooth programming,based on the conceptions of uniform(Fb,ρ)-convex,uniform(Fb,ρ)-pseudoconvex,and uniform(Fb,ρ)-quasiconvex functions,a class of nonsmooth fractional semi-infinite programming involving these generalized convexity are researched.Some sufficient optimality conditions for the above nonsmooth fractional semiinfinite programming are proved by reduction to absurdity method.