摘要
本文总假定:R^n为n维欧氏空间,R为全体实数,D(?)R^n为开子集,‖·‖为R^n中的欧氏模,co为凸包,co为闭凸包,f:R^n→R为R^n上的实值函数。
Firstly,we define a class of quasi-Lipschitz functions which includes the Lipschitz functions and give some simple properties of the quasi-Lipschitz functions.Secondly,we establish a type of new generalized differential theory in the manner completely different from those in which Clarke,Ioffe and Aubin defined generalized gradients.Finally,we give some simple applications of our generalized gradients to optimization.
出处
《应用数学学报》
CSCD
北大核心
1992年第4期499-509,共11页
Acta Mathematicae Applicatae Sinica
基金
国家自然科学基金
