非光滑函数的半严格拟不变凸性  

Semistrictly Quasi-Invexity of Nonsmooth Functions

作　　者：刘彩平[1] 

机构地区：[1]重庆师范大学数学与计算机科学学院

出　　处：《重庆师范大学学报（自然科学版）》2007年第3期1-3,16,共4页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金(No.10471159)

摘　　要：在Banach空间中定义了一种新的广义凸函数——半严格拟不变凸函数。举例说明了半严格拟不变凸函数是比拟不变凸函数和伪不变凸函数更为广泛的一类广义凸函数。对于非光滑的半严格拟不变凸函数,讨论了它的C larke广义次微分性质。讨论了半严格拟不变凸函数与拟不变凸函数之间的关系。此外,在这篇文章里,还给出了半严格拟不变凸函数的两个基本性质。本文的结果扩充了无限维空间中的凸性理论。In this paper a new class of generalized convex functions in Banach Space, termed as semistrictly quasi-invex functions, is introduced. We give examples to illustrate that semistrictly quasi-invex functions are more wider than quasi-invex functions and pseudo-invex functions. The properties of nonsmooth semistrictly quasi-invex functions for corresponding Clarke＇s subdifferential are discussed. In particular, the relationships are investigated between semistrictly quasi-invex functions and quasi-invex functions. Moreover, two basic properties of semistrictly quasi-invex functions are given. Our results extend the theory of generalized convexity in infinite dimension space.

关 键 词：半严格拟不变凸函数 拟不变凸函数 伪不变凸函数 非光滑 

分 类 号：O221.2[理学—运筹学与控制论]