| 半严格-G-E-半预不变凸型函数及其在数学规划中的应用研究 |
| |
| 引用本文： | 彭再云,孙佳徽,李科科,张石生.半严格-G-E-半预不变凸型函数及其在数学规划中的应用研究[J].应用数学和力学,2017,38(7):827-836. |
| |
| 作者姓名： | 彭再云 孙佳徽 李科科 张石生 |
| |
| 作者单位： | 1重庆交通大学 数学与统计学院, 重庆 400074;2西安工程大学 管理学院, 西安 710048;3重庆师范大学 数学科学学院, 重庆 401331;4云南财经大学 数学与统计学院, 昆明 650224 |
| |
| 基金项目： | 2016T90837)国家自然科学基金(11471059;11431004)，重庆市基础与前沿研究项目(cstc2017jcyjAX0382;cstc2016jcyjA0219)，重庆市民生项目(cstc2015shmszx30004)，中国博士后科学基金(2015M580774;2016T90837)，重庆市高校创新团队项目(CXTDX201601022) |
| |
| 摘 要： | 提出了一类新的广义凸函数——半严格-G-E-半预不变凸函数,它是一类非常重要的广义凸函数,为半严格-G-半预不变凸函数与半严格-E-预不变凸函数的推广.首先给出例子,以说明半严格-G-E-半预不变凸函数的存在性及其与其他相关广义凸函数间的关系.然后讨论了半严格-G-E-半预不变凸函数的一些基本性质.最后,探究了半严格-G-E-半预不变凸型函数分别在无约束和有约束非线性规划问题中的重要应用,获得一系列最优性结论,并举例验证了所得结果的正确性.
|
| 关 键 词： | E-半连通集 半严格-G-E-半预不变凸函数 性质 非线性规划 应用 |
| 收稿时间： | 2016-09-13 |
Study of Semistrict-G-E-Semipreinvex Functions and Applications in Nonlinear Programming |
| |
| PENG Zai-yun,SUN Jia-hui,LI Ke-ke,ZHANG Shi-sheng.Study of Semistrict-G-E-Semipreinvex Functions and Applications in Nonlinear Programming[J].Applied Mathematics and Mechanics,2017,38(7):827-836. |
| |
| Authors: | PENG Zai-yun SUN Jia-hui LI Ke-ke ZHANG Shi-sheng |
| |
| Institution: | 1College of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing 400074, P.R.China;2School of Management, Xi’an Polytechnic University, Xi’an 710048, P.R.China;3School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, P.R.China;4School of Statistics and Mathematics,Yunnan University of Finance and Economics, Kunming 650224, P.R.China |
| |
| Abstract: | A new class of generalized convex functions,namely the semistrict-G-E-semipreinvex functions were proposed,which are a class of very important generalized convex functions and make a true generalization of both the semistrict-G-semipreinvex functions and the semistrict-E-preinvex functions.Firstly,several examples were given to illustrate the existence of semistrict-G-E-semipreinvex functions and the dependence on the related generalized convex functions.Afterwards,the basic characteristics of the semistrict-G-E-semipreinvex functions were discussed.Finally,some applications of the semistrict-G-E-semipreinvex functions in nonlinear programming problems without constraint and with inequality constraints were studied respectively,and some optimality results were obtained;moreover,some examples were given to illustrate the correctness of the obtained results. |
| |
| Keywords: | E-semi-connected set semistrict-G-E-semipreinvex function characteristics nonlinear programming application |
| 本文献已被 CNKI 万方数据 等数据库收录！ |
| 点击此处可从《应用数学和力学》浏览原始摘要信息 |
| 点击此处可从《应用数学和力学》下载免费的PDF全文 |
|
