向量D-η-E-半预不变凸映射与向量优化  

D-η-E-Semipreinvex Vector Mappings and Vector Optimization

作　　者：彭再云[1] 李科科[1,2] 张石生[3] 

机构地区：[1]重庆交通大学理学院,重庆400074 [2]重庆师范大学数学学院,重庆400047 [3]云南财经大学数学与统计学院,昆明650224

出　　处：《应用数学和力学》2014年第9期1020-1032,共13页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11301571;11271389);重庆市自然科学基金(CSTC2012jjA00016);重庆市教委科技项目(KJ130428)~~

摘　　要：提出了一类新的向量值映射——D-η-E-半预不变凸映射,它是E-预不变凸映射与D-η-半预不变凸映射的真推广.首先,用例子说明了E-半不变凸集、D-η-E-半预不变凸映射的存在性;然后,给出了D-η-E-半预不变凸映射的判定定理,并讨论了D-η-E-半预不变凸映射与D-η-E-严格/半严格半预不变凸映射的关系;最后,得到了D-η-E-半严格半预不变凸映射在隐约束优化问题中的一个重要应用,并举例验证了所得结果.A class of new vector valued generalized convex mappings--D-η-E-semipreinvex mappings, as a true generalization of the E-preinvex mappings and the D-η-semipreinvex map- pings, were given. First, several examples were presented to show the existence of the E-semiinvex sets and the D-y-E-semipreinvex mappings. Second, a decision criterion for the D-η-E- semipreinvex mappings was introduced, and the relationships among the D-~q-E-semipreinvexity, the D-η-E- strict semipreinvexity and the D-η-E- semistrict semipreinvexity were discussed. Finally, an important application of the D-η-E-semistrictly semipreinvexity to vector optimization with implicit constraint was discussed, then some examples were given to prove the main conclusions.

关 键 词：E-半不变凸集 D-η-E-半预不变凸映射 判定定理 优化问题 应用 

分 类 号：O221.1[理学—运筹学与控制论]