<em>D-η</em>-半预不变凸映射的性质与应用

彭再云; 王堃颍; 赵勇; 张石生

doi:10.3879/j.issn.1000-0887.2014.02.008

D-η-半预不变凸映射的性质与应用

doi: 10.3879/j.issn.1000-0887.2014.02.008

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 401331;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(11271389; 11301571); 重庆市自然科学基金(CSTC2012jjA00016); 重庆市教委基金(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)

中图分类号: O221.1
计量
- 文章访问数: 1330
- HTML全文浏览量: 114
- PDF下载量: 891
- 被引次数: 0
出版历程
- 收稿日期: 2013-07-16
- 刊出日期: 2014-02-15

Characterizations and Applications of D-η-Semipreinvex Mappings

¹School of Science, Chongqing Jiaotong University, Chongqing 400074, P.R.China;²School of Mathematics Science, Chongqing Normal University, Chongqing 401331, P.R.China;³Department of Statistics and Mathematics,Yunnan University of Finance and Economics, Kunmin 650224, P.R.China

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

摘要

摘要: 提出了一类新的向量值映射——D-η-半预不变凸映射,它是D-预不变凸映射的真推广.首先,用例子说明了D-η-半预不变凸映射的存在性,并说明其区别于D-η-半严格半预不变凸映射；然后，给出了D-η-半预不变凸映射的判定定理,并建立了D-η-半预不变凸映射与D-η-严格/半严格半预不变凸映射间的关系；最后,讨论了D-η-半严格半预不变凸映射在优化问题中的应用，并举例验证了所得结论的正确性.
- D-&eta /
- -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-semipreinvex mappings, which was a true generalization of D-preinvex mapping, was given. Firstly, examples were given to show the existence of D-η-semipreinvexmappings and illustrate the differences between D-η-semistrictly semi-preinvex and D-η-semipreinv exmapping. Secondly, a criterion of D-η-semipreinv exity was given, and the relationships among D-η-semipreinvexity, D-η-strict semipreinvexity and D-η-semistrict semipreinvexity were discussed. Finally, an important application of D-η-semistrict semipreinvexity in vector optimization was discussed, then give an example was given to illustrate the result.
- D-&eta /
- -semipreinvex mappings /
- criterion /
- vector optimization /
- applications

HTML全文

参考文献(13)

[1]	Hanson M A. On sufficiency of the Kuhn-Tucker conditions[J]. Journal of Mathematical Analysis and Applications,1981,80(2): 545-550.
[2]	Ben-Israel A, Mond B. What is invexity?[J]. Journal of the Australian Mathematical Society, 1986,28: 1-9.
[3]	Weir T, Jeyakumar V. A class of nonconvex functions and mathematical programming[J]. Bulletin of Australian Mathematical Society,1988,〖STHZ〗 38: 177-189.
[4]	Yang X M, Li D. On properties of preinvex functions[J]. Journal of Mathematical Analysis and Applications, 2001,256(1): 229-241.
[5]	Yang X M, Li D. Semistrictly preinvex functions[J]. Journal of Mathematical Analysis and Applications, 2001,258(1): 287-308.
[6]	Yang X Q, Chen G Y. A class of nonconvex functions and pre-variational inequalities[J]. Journal of Mathematical Analysis and Applications,1992,169(2): 359-373.
[7]	Peng Z Y, Chang S S. Some properties of semi-G-preinvex functions[J]. Taiwanese Journal of Mathematics,2013,17(3): 873-884.
[8]	Antczak T. G-pre-invex functions in mathematical programming[J]. Journal of Computational and Applied Mathematics,2008,217(1): 212-226.
[9]	Kazmi K R. Some remarks on vector optimization problems[J]. Journal of Optimization Theory and Applications,1998,96(1): 133-138.
[10]	Peng J W, Zhu D L. On D-preinvex type functions[J]. Journal of Inequalities and Applications,2006, Article ID 93532: 1-14.
[11]	Long X J, Peng Z Y, Zeng B. Remark on cone semistrictly preinvex functions[J]. Optimization Letters,2009,3(3): 337-345.
[12]	彭建文. 向量值映射D-η-预不变真拟凸的性质[J]. 系统科学与数学, 2003,23(3): 306-314.(PENG Jian-wen. Properties of D-η-properly prequasi-invex functions[J]. Journal of Systems Science and Mathematical Sciences,2003,23(3): 306-314.(in Chinese))
[13]	彭建文. 广义凸性及其在最优化问题中的应用[D]. 博士学位论文. 呼和浩特: 内蒙古大学理工学院, 2005.(PENG Jian-wen. Generalized convexity with application optimization problems[D]. Ph D Thesis. Hohhot: Inner Mongolia University, 2005.(in Chinese))