关于向量优化问题的Δ函数标量化刻画的某些注记

唐莉萍; 李飞; 赵克全; 杨新民

doi:10.3879/j.issn.1000-0887.2015.10.009

关于向量优化问题的Δ函数标量化刻画的某些注记

doi: 10.3879/j.issn.1000-0887.2015.10.009

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

基金项目: 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)

详细信息

作者简介:
唐莉萍（1985—），女，四川资中人，博士生（通讯作者. E-mail: tanglipings@163.com）;李飞（1981—），男，内蒙古巴彦淖儿人，讲师，博士生（E-mail: lifeimath@163.com）;赵克全（1979—），男，四川南充人，副教授，博士（E-mail: kequanz@163.com）;杨新民（1960—），男，四川泸州人，教授，博士生导师（E-mail: xmyang@cqnu.edu.cn）.

中图分类号: O221.6
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出版历程
- 收稿日期: 2015-01-14
- 修回日期: 2015-08-13
- 刊出日期: 2015-10-15

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

¹College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, P.R.China;²School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, P.R.China;³School of Mathematical Sciences, Chongqing Normal University, Chongqing 400047, P.R.China

Funds: The National Natural Science Foundation of China(Key Program)(11431004);The National Natural Science Foundation of China（General Program）(11271391;11201511;11301574)

摘要

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.
- 向量优化 /
- 近似真有效解 /
- Δ函数 /
- 非线性标量化
Abstract: Recently，Xia Yuan-mei,et al.(Journal of Chongqing Normal University(Natural Science), 2015,32(1): 12-15) studied the ?-properly efficient solutions to vector optimization problems via scalar function Δ in terms of the nonlinear scalarization method, and gave some examples to illustrate their results. It was point out here that theorem 1 established by Xia Yuan-mei,et al. was a special case of Theorem 4.6(i) obtained by Gao, et al.(Journal of Industrial 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 scalarization of function Δ 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 ?-properly efficient solutions did exist, were given to illustrate the main results.
- vector optimization /
- approximate properly efficient solution /
- function Δ /
- nonlinear scalarization

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参考文献(23)

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