α-E-半预不变凸型函数的性质与多目标规划的最优性条件  

Properties of α-E-Semi-preinvex Convex Functions and Optimality Conditions for Multi-Objective Programming

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)

机构地区：[1]重庆交通大学数学与统计学院,重庆400074

出　　处：《重庆师范大学学报（自然科学版）》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)。

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.

关 键 词：α-E-半预不变凸函数 性质 多目标规划 最优性条件 

分 类 号：O224[理学—运筹学与控制论]