α-D-半预不变凸映射与最优化  

α-D-Semi-Preinvex Mappings and Optimization

作　　者：彭志莹 彭再云 陈雪静 邓春艳 PENG Zhiying;PENG Zaiyun;CHEN Xuejing;DENG Chunyan(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）》2022年第1期9-18,共10页Journal of Chongqing Normal University:Natural Science

基　　金：重庆市高校创新研究群体项目(No.CXQT21021);重庆市自然科学基金面上项目(No.cstc2021jcyjmsxmX0080);重庆交通大学院级研究生科研创新基金(No.2021ST003);重庆交通大学校级研究生科研创新基金(No.2021S0062)。

摘　　要：【目的】提出了一类新的向量值映射,即α-D-半预不变凸映射,研究了此类映射的判定定理、性质以及该类映射在优化问题中的应用。【方法】理论推导并举例进行验证,利用向量值映射的半连续性获得α-D-半预不变凸型映射的相关结论。【结果】首先给出了α-D-半预不变凸映射的定义,并用实例说明了α-D-半预不变凸映射的存在性;然后获得了α-D-半预不变凸映射的判定定理和两个性质;最后讨论了α-D-半严格半预不变凸映射在向量优化问题中的应用,并举例说明所得结果的正确性。【结论】α-D-半预不变凸映射在一定程度上丰富了广义凸向量值映射及最优化理论的研究。[Purposes]It presents a new class of vector valued generalized convex mappings,α-D-semi-preinvex mappings,and its decision theorem,properties and application in optimization problems are studied.[Methods]The relevant conclusions of theα-D-semi-preinvex mappings are obtained by using the semi-continuity of the vector-valued mappings.[Findings]First,the definition ofα-D-semi-pre-invex mappings is given and its existence is illustrated by examples;then the decision theorem and two properties ofα-D-semi-pre-invex mappings are obtained;finally,the application ofα-D-semi-strict semi-preinvex mappings in vector optimization problems is discussed and the correctness of the results is verified by examples.[Conclusions]α-D-semi-pre-invex mappings enriches the study of generalized convex vector-valued mappings and optimization theory.

关 键 词：α-D-半预不变凸映射 判定定理 向量优化 应用 

分 类 号：O224[理学—运筹学与控制论]