摘要
【目的】提出了一类新的广义凸函数,即α-E-半预不变凸函数,研究了α-E-半预不变凸函数的一些性质以及它在多目标规划中的应用。【方法】理论推导和例子验证相结合。【结果】α-E-半预不变凸函数的线性组合是α-E-半预不变凸函数;讨论了α-E-半预不变凸函数在约束条件下的多目标规划问题的最优性条件,得到了多目标规划问题的可行解集是α-E-半不变凸集以及多目标规划问题的局部有效解与全局有效解的关系;最后,利用方向导数获得了关于多目标规划问题有效解的一个充要条件。【结论】α-E-半预不变凸函数是大量存在的,它在数学规划研究中具有重要意义,丰富了数学规划相关方向的研究。
[Purposes]It presents a new class of generalized convex functions:α-E-semi-preinvex convex function.The properties of α-E-semi-preinvex convex functions is studied and multi-objective programming is applied.[Methods]Combine theoretical derivation with example validation.[Findings]The linear combination of α-E-semi-preinvex convex functions is α-E-semi-preinvex convex functions.The optimality condition of multi-objective programming problem with α-E-semi-preinvex convex functions are discussed under constraints.The feasible solution set of multi-objective programming problem is α-E-semi-preinvex convex set.The relationship between local and global efficient solutions for multi-objective programming problems.Finally,a sufficient and necessary condition for the effective solution of the multi-objective programming problem can be obtained by the directional derivative.[Conclusions]α-E-semi-preinvex convex function is a large number of existence.It is of great significance in the study of mathematical planning and enriches the research on the related direction of mathematical planning.
作者
陈雪静
彭再云
邵重阳
胡灿
CHEN Xuejing;PENG Zaiyun;SHAO Chongyang;HU Can(College of Mathematics and Statistics,Chongqing Jiaotong University,Chongqing 400074,China)
出处
《重庆师范大学学报（自然科学版）》
CAS
北大核心
2020年第1期91-98,共8页
Journal of Chongqing Normal University:Natural Science
基金
国家自然科学基金(No.11301571)
重庆市基础与前沿研究项目(No.cstc2018jcyjAX0337)
重庆市巴渝学者计划资助项目
重庆市留创计划创新项目(No.cx2019148)
重庆市运筹与控制论重点实验室开放课题(No.CSSXKFKTZ201801)
重庆市大学生创新创业项目(No.S201910618026)。
关键词
α-E-半预不变凸函数
性质
多目标规划
最优性条件
α-E-Semi-preinvex convex function
character
multi-objective programming
optimality conditions
