向量值D-E-预不变真拟凸映射研究  

THE STUDY OF VECTOR-VALUED D-E-PROPERLY PREQUASI-INVEX MAPPINGS

作　　者：彭再云[1] 李科科[2,1] 范琳煊 

机构地区：[1]重庆交通大学数学与统计学院,重庆400074 [2]重庆师范大学数学科学学院,重庆401331

出　　处：《系统科学与数学》2016年第8期1298-1307,共10页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(11271389,11301571);重庆市自然科学基金(cstc2015jcyjA00025,2014pt-sy00001);国家博士后科学基金(2015M580774,2016T90837);重庆市研究生科研创新训练项目(CYS16144)资助课题

摘　　要：提出了一类新的向量值映射-D-E-预不变真拟凸映射,它是E-预不变凸映射(Fulga和Preda,2009)与D-预不变真拟凸映射(彭建文,2003)的真推广.首先,用例子说明E-不变凸集,D-E-预不变真拟凸映射的存在性;然后,讨论D-E-预不变真拟凸映射的性质,并获得D-E-半严格预不变真拟凸映射在向量优化问题中的一个重要应用;最后,对D-E-半严格预不变真拟凸与D-E-预不变真拟凸映射之间的关系做了探究,并举例验证了所得结果.A class of new vector-valued generalized convex mapping-D-E-properly prequsai-invex mapping, which is a true generalization of E-preinvex mapping （Fulga and Preda, 2009） and D-properly prequasi-invex mapping （Peng, 2003）, is discussed in this paper. Firstly, examples are given to show the existence of E-invex sets and D-E-properly prequasi-invex mappings. Secondly, characterizations of D-E-properly prequsai-invex mappings and an important application of D-E-properly semistrictly prequasi-invexity in vector optimization are obtained. Finally, relationships between D-E-properly semistrictly prequasi-invexity and D-E-properly prequasi-invexity are discussed, then some examples are given to illustrate the obtained results.

关 键 词：E-不变凸集 D—E-预不变真拟凸映射 向量优化问题 

分 类 号：O224[理学—运筹学与控制论]