回收函数与函数的无界性  

Recession Functions and Unboundedness of Functions

作　　者：李美术 高英 LI Mei-shu GAO Ying(School of Mathematical Sciences, Chongqing Normal University, Chongqing 400047, P.R. Chin)

机构地区：[1]重庆师范大学数学科学学院,重庆400047

出　　处：《应用数学和力学》2017年第10期1187-1194,共8页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11201511;11771064);重庆市科委项目(cstc2015jcyj A00005);重庆市教委项目(KJ1500309)~~

摘　　要：主要利用回收锥和回收函数来研究函数的下无界性.首先,针对凸函数在非可微条件下,利用中值定理和回收锥刻画了凸函数次微分的性质,并在此基础上给出了基于次可微条件下回收向量的充要条件.其次,将凸性推广到E-凸,在一定条件下,利用回收函数研究了E-凸函数的下无界性.最后,通过举例说明这些结果不能推广到拟凸条件.The unboundedness of functions was investigated with the recession cones and recession functions.Firstly,the mean value theorem and recession cones were used to characterize the subdifferentials of convex functions on condition of nondifferentiability. Based on the above results,the necessary and sufficient conditions for recession functions under the subdifferentiable assumption were given. Secondly,the convexity was generalized to E-convex functions,and the unbounded feature of E-convex functions was studied by means of recession functions under the special sub-linear assumption. Finally,an example was given to indicate that these results can not be extended to quasiconvex functions.

关 键 词：回收锥 回收函数 广义凸函数 次微分 下无界 

分 类 号：O174[理学—数学]