半B-(E,F)-凸约束单目标规划的最优性条件

Semi B-(E,F)-convex Constrained Single-objective Programming of Optimal Conditions

广义凸性和凸性在数学规划最优化理论以及最优化控制等很多数学领域中具有十分重要的作用,但凸性的局限性也是很显然的。可以说对于凸性和广义凸性的研究是数学规划的主要方向。基于B-凸性和半(E,F)-凸性,提出了一类新的广义凸性:半B-(E,F)-凸性,给出了半B-(E,F)-凸函数的概念,利用半B-(E,F)-凸函数的有关性质讨论了半B-(E,F)-凸函数单目标规划的最优性条件。

Convexity and generalized in the convexity of mathematical programming optimization theory,optimization control and many other areas of mathematics plays an important role,but the limitations of convexity are also very obvious.This paper generalized two kinds of convex functions：B-convex function and semi-（E,F）-convex function are researched furtherly.A new kind of generalized convexity：semi-B-（E,F）-convexity is introduced,semi-B-（E,F）-convex function and its generalized convexity are introduced,this paper presents the optimal conditions of single-objective programming for semiB-（E,F）-convexity functions using properities of semiB-（E,F）-convexity functions.