关于半B-(E,F)-凸约束多目标规划的一个对偶定理  

Duality Theorems of Single Objective Programming for Semi B-(E,F)-convex Functions

作　　者：马晓娜[1] 

机构地区：[1]宿州学院数学与统计学院,安徽宿州234000

出　　处：《宜春学院学报》2014年第9期29-31,共3页Journal of Yichun University

基　　金：宿州学院科研平台开放课题(项目编号:2012YKF32)

摘　　要：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,因此对凸性的研究和广义凸性的探索一直是凸分析的重要课题也是数学规划最重要的内容之一。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,提出了半B-(E,F)-凸规划的概念,利用半B-(E,F)-凸规划的有关性质,讨论了半B-(E,F)-凸函数多目标规划的弱对偶定理。Convexity and generalized in the convexity of mathematical programming optimization theory and optimi- zation theory and many other areas of mathematics plays an important role, Therefore, the research on convexity and generalized convexity has been one of the important aspects in mathematical programming. In this thesis, two classes of generalized convex functions ： B - convex function and semi - （ E, F） - convex function are researched furtherly. First, a new class of generalized convexity ： B - semi - B - （E, F） - convexity is introduced, Semi B - （E,F） - convex function and its generalized convexity are introduced, and puts forward the concept of semiB - （E,F）- convex programming. This paper presents the weak duality theorem of multi -objective programming for semiB - （E, F） - convex function through using properities of semiB - （E,F）- convex programming.

关 键 词：半B-(E F)-凸函数 多目标规划 对偶性 

分 类 号：O221.6[理学—运筹学与控制论]