摘要
研究一类广义凸多目标分式规划(Multi-objective Fractional Programming)问题(MFP)近似弱有效解的最优性条件和鞍点定理。首先,利用参数化方法将问题(MFP)转化成为一个多目标非分式规划(Multi-objective Non-fractional Programming)问题(MNP)。其次,针对问题(MNP)的目标和约束函数,引入type-I函数和近似伪拟-type-I函数的概念,并给出实例说明了它们的存在性。最后,在新引人的两种广义凸性假设下,得到了问题(MNP)关于近似弱有效解的最优性条件和鞍点定理。
The aim of this paper is to study the optimality conditions and saddle point theorems of a class of generalized convex(multi-objective fractional programming)problem(MFP)with respect to approximate weakly efficient solutions.Firstly,by using parameter method,the problem(MFP)is transformed into a(multi-objective non-fractional programming)proble(MNP).Secondly,the concepts of type-I function and approximate pseudo-quasi-type-I function are introduced for the objective and constraint functions of problem(MNP).Finally,under assumptions of the introduced generalized convexities,the optimality conditions and saddle point theorems to problem(MNP)are established.
作者
韩文艳
余国林
HAN Wenyan;YU Guolin(Institute of Applied Mathematics,North Minzu University,Yinchuan 750021,China)
出处
《南昌大学学报（理科版）》
CAS
北大核心
2020年第2期107-112,共6页
Journal of Nanchang University(Natural Science)
基金
国家自然科学基金资助项目(11861002)
宁夏自然科学基金资助项目(NZ17112)
北方民族大学重大专项(ZDZX201804)。
关键词
多目标分式规划
近似弱有效解
广义凸函数
最优性条件
鞍点
Multi-objective fractional programming
Approximate weak efficient solution
Generalized convex function
Optimality conditions
Saddle point
