次b凸函数和次b凸规划

摘要

研究一种称为次b凸函数的广义凸函数,并介绍了次b凸集的概念.分别在一般情形及可微情形下讨论了次b凸函数的相关性质,得到了次b凸函数成为拟凸函数及伪凸函数的充分条件.最后,在次b凸函数的条件下给出了无约束及带不等式约束规划的最优性条件.%The paper studied a new generalized convex function which called sub-bconvex function,and introduced a new concept of sub-b-convex set.The basic properties of sub-b-convex functions were discussed in general case and differentiable case,respectively.And,obtained the sufficient conditions that the sub-b-convex function become quasi-convex function or pseudo-convex function.Furthermore,the sufficient conditions of optimality for unconstrained and inequality constrained programming were obtained under the sub-b-convexity.