关于向量优化问题的Δ函数标量化刻画的某些注记  

Some Notes on the Scalarization of Function Δ for Vector Optimization Problems

作　　者：唐莉萍[1] 李飞[2] 赵克全[3] 杨新民[3] 

机构地区：[1]重庆工商大学数学与统计学院,重庆400067 [2]内蒙古大学数学科学学院,呼和浩特010021 [3]重庆师范大学数学科学学院,重庆400047

出　　处：《应用数学和力学》2015年第10期1095-1106,共12页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(重点项目)(11431004);国家自然科学基金(面上项目)(11271391;11201511;11301574);重庆市科委项目(cstc2014pt-sy00001)~~

摘　　要：近期,夏远梅等(重庆师范大学(自然科学版),2015,32(1):12-15)利用Δ函数通过非线性标量化方法研究了向量优化问题的∈-真有效解并举例说明了主要结果.笔者指出:其定理1是Gao等(Journal of Industrial and Management Optimization,2011,7(2):483-496)建立的定理4.6(i)的特例;其定理2的证明存在不足.通过研究一般的(C,ε)-真有效解的Δ函数非线性标量化,给出了定理2的严谨证明.最后,在∈-真有效解存在的情况下举例说明了主要结果.Recently, XIA Yuan-mei, et al. （ Journal of Chongqing Normal University （ Natural Science）, 2015, 32（ 1 ） ： 12-15） studied the ε- properly efficient solutions to vector optimization problems via scalar function A in terms of the nonlinear scalarization method, and gave some examples to illustrate their results. It was point out here that theorem l established by XIA Yuan-mei, et al. was a special case of theorem 4.5（i） obtained by Gao, et al. （Journal of In- dustrial and Management Optimization, 2011, 7（2）： 483-496）, and the proof of theorem 2 given by XIA Yuan-mei, et al. had some deficiency. Through investigation the nonlinear scalar- ization of function A for the （ C, ε）- properly efficient solutions, theorem 2 obtained by XIA Yuan-mei, et al. was proved again rigorously. In the end, some examples in which e- properly efficient solutions did exist, were given to illustrate the main results.

关 键 词：向量优化 近似真有效解 Δ函数 非线性标量化 

分 类 号：O221.6[理学—运筹学与控制论]