广义凸多目标规划的最优性

On Optimality of Generalized Convex Multi-objective Programming

借助Clarke广义梯度以及凸泛函的相关性质,给出了一些新的广义凸函数:广义(C,α)-Ⅰ型凸函数、广义严格拟(C,α)-Ⅰ型凸函数以及广义严格拟伪(C,α)-Ⅰ型凸函数.在新的广义凸性下,得到了一类多目标规划问题的若干最优性充分条件.

With the help of the Clarke generalized gradient and the related properties of convexfunctionals, some generalized convex functions have been given: generalized(C,α)-type Ⅰ convex functions, generalized strict quasi-(C,α)-type Ⅰ convex functions, and generalized strict quasi-pseudo-(C,α)-type Ⅰ convex functions. Under these new generalized convexities, some sufficient condition of optimality for a class of multi-objective programming problems have been obtained.