F-G广义凸函数与F拟凸函数  

The F-G Generalized Convex and F Quasi Convex Functions

作　　者：黄金莹[1] 赵宇[1] 方秀男[1] 

机构地区：[1]佳木斯大学理学院数学系,黑龙江佳木斯154007

出　　处：《重庆师范大学学报（自然科学版）》2011年第4期1-5,共5页Journal of Chongqing Normal University:Natural Science

基　　金：黑龙江省教育厅科学技术研究项目(No.11551499)

摘　　要：给出F-G广义凸函数和F拟凸函数等概念及特例,利用条件P1,P2,研究了F-G广义凸函数的若干性质,给出了由F-G广义凸函数构造的函数Φ(λ)=f[F(x,y,λ)]在[0,1]上是(拟)凸函数和水平集Sη(f)={x x∈K,f(x)≤η}是关于F的广义凸集等结论,并指出f在K上是F-G广义凸函数的充分必要条件是f在K上既是F-G近似广义凸函数也是F拟凸函数,最后给出了半严格F拟凸函数在极小化问题中的应用,指出当limλ→0 F(x,y,λ)=y时,半严格F拟凸函数的局部最优解是全局最优解。Given in this paper are the definitions of F-G generalized convex thnctions, Fquasi convex lunctlons and their examples, By using the conditions P1 and P2, the author gives some properties of F-G generalized convex functions, gives functions Ф（λ）=f[F（x,y,λ）] which was made by F-G generalized convex functions be （quasi） convex function on [ 0,1 ], gives Sη（f）={x｜x∈K,f（x）≤η} is generalized convex sets about F and givesf is F-G generalized convex functions over K if and only iff is F-G approximately generalized convex functions and F quasi convex functions over K. At last, the author gives the applications of semi-strictly F quasi convex functions in minimization problem and gives when limF（ x ,y ,λ ） = y, then local optima solution of semi-stricdy F quasi convex functions is global optimal solution.

关 键 词：F-G广义凸函数 f拟凸函数 条件P1 条件P2 半严格F拟凸函数 

分 类 号：O174.13[理学—数学]