强G-半预不变凸性与非线性规划问题  

Strongly Semi-G-preinvexity and Nonlinear Programming

作　　者：彭再云[1] 孔祥茜[1,2] 

机构地区：[1]重庆交通大学理学院,重庆400074 [2]吉林大学管理学院,吉林长春130022

出　　处：《广西师范大学学报（自然科学版）》2013年第1期48-53,共6页Journal of Guangxi Normal University:Natural Science Edition

基　　金：国家自然科学基金资助项目(11271389);国家青年基金资助项目(11201509);重庆市自然科学基金资助项目(CSTC2011AC6104;2012jjA00016);重庆市教委基金资助项目(KJ120401)

摘　　要：本文提出一类新的广义凸函数——强G-半预不变凸函数,它是一类重要的广义凸函数,是半预不变凸函数与强G-预不变凸函数的真推广。首先,用例子验证强G-半预不变凸函数的存在性,并举例说明它区别于强预不变凸函数;然后探讨强G-半预不变凸函数的性质与几何刻画;最后,给出强G-半预不变凸函数在非线性规划中的几个应用,得到了一些最优性结果,并举例验证结论的正确性。A class of new generalized convex function,strongly semi-G-preinvex function,Is given in theis paper. It is an important class of generalized convex function. It is a true generalization of semi-preinvex functions and strongly G-preinvex functions. First,an example is given to show that there exists strongly semi-G-preinvex function. At the same time,an example is given to show that strongly semi-G-preinvex function is different from strongly preinvex functions. Then,some properties of strongly semi-G-preinvex functions are discussed. Finally ,some optimal results are obtained in nonlinear programming problems, and an example is also given for illustration of the corresponding results.

关 键 词：半连通集 非线性规划 强预不变凸函数 强G-半预不变凸函数 

分 类 号：O221.1[理学—运筹学与控制论]