应用数学和力学2017，Vol.38Issue(7)：827-836,10.DOI:10.21656/1000-0887.370280
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
Study of Semistrict-G-E-Semipreinvex Functions and Applications in Nonlinear Programming
摘要
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.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Key words
E-semi-connected set/semistrict-G-E-semipreinvex function/characteristics/nonlinear programming/application分类
数理科学引用本文复制引用
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):827-836,10.基金项目
The National Natural Science Foundation of China(11471059 （）
11431004) （）
China Postdoctoral Science Foundation(2015M580774 （）
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) （cstc2015shmszx30004）
中国博士后科学基金(2015M580774 （）
2016T90837) （）
重庆市高校创新团队项目(CXTDX201601022) （CXTDX201601022）
