E-预不变凸区间值函数及其在数学规划中的应用  

E-Preinvex Interval-Valued Function and Its Application in Mathematical Programming

作　　者：邓春艳 彭再云 陈雪静 彭志莹 DENG Chunyan;PENG Zaiyun;CHEN Xuejing;PENG Zhiying(School of Mathematicaland Statistics,Chongqing Jiaotong University,Chongqing 401331,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）》2021年第1期30-38,共9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);最优化与控制教育部重点实验室开放基金重点课题(No.CSSXKFKTZ201801);重庆市研究生科研创新项目(No.CYS20290);重庆市研究生导师团队建设项目(No.JDDSTD201802)。

摘　　要：【目的】提出并研究了在LU-序关系下的E-预不变凸区间值函数。【方法】首先给出了LU-E-预不变凸区间值函数和LU-E-不变凸区间值函数的定义,举例验证了LU-E-预不变凸区间值函数的存在性;其次讨论了LU-E-预不变凸区间值函数与其他几类区间值函数间的关系;最后研究了一类LU-E-预不变凸区间值优化问题,给出了E-type-Ⅰ型最优解和E-type-Ⅱ型最优解的概念,并证明了E-KKT最优性条件的必要性和充分性条件。【结果】基于LU-序关系,理论推导并举例验证。【结论】文中将近期关于广义凸函数的一些研究成果进行了推广,在一定程度上丰富了广义凸函数的研究。[Purposes]Here it mainly studies the correlation properties of LU-E-preinvex interval-valued function under LU-order relations and its application in mathematical programming.[Methods]On the basis of order relations,the theory is deduced and verified with examples.[Findings]Firstly,the definition of the LU-E-preinvex interval-valued function and the LU-E-convex interval value function is given.And the existence of the LU-E-preinvex interval-valued function is verified by example.Secondly,the relationship between LU-E-preinvex interval-valued function and other interval valued functions is discussed.Finally,the LU-Epreinvex interval-valued optimization problem is studied and the concept of E-type-Ⅰ optimal solution and the E-type-Ⅱ optimal solution for generalized convex interval-valued optimization problems is given.And it proved that the E-KKT optimality conditions of necessity and sufficiency conditions.[Conclusions]Some recent research results on generalized convex functions are generalized,which enriches the research on generalized convex functions to some extent.

关 键 词：LU-E-预不变凸区间值函数 E-不变凸 E-KKT最优性 

分 类 号：O221[理学—运筹学与控制论]