向量<em>D-<strong>η</strong>-E</em>-半预不变凸映射与向量优化

彭再云; 李科科; 张石生

doi:10.3879/j.issn.1000-0887.2014.09.008

向量D-η-E-半预不变凸映射与向量优化

doi: 10.3879/j.issn.1000-0887.2014.09.008

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

基金项目: 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)

详细信息

作者简介:
彭再云(1980—)，男，重庆人，副教授，博士(E-mail: pengzaiyun@126.com);张石生(1934—)，男，云南曲靖人，教授(通讯作者. E-mail: changss@yahoo.cn).

中图分类号: O221.1
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出版历程
- 收稿日期: 2014-04-05
- 刊出日期: 2014-09-15

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

Funds: The National Natural Science Foundation of China(11301571; 11271389)

摘要

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.
- 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
Abstract: 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 mappings, were given. First, several examples were presented to show the existence of the E-semi-invex sets and the D- η -E-semipreinvex mappings. Second, a decision criterion for the D- η -E-semipreinvex mappings was introduced, and the relationships among the D- η -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.
- E-semi-invex set /
- D-η-E-semipreinvex mapping /
- decision criterion /
- vector optimization /
- application

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参考文献(15)

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