摘要
本文对严格拟单调进行推广,定义了严格不变拟单调:设K为Rn中的不变凸集,η:Rn×Rn→Rn,如果f是不变拟单调的,且对x,y∈K,x≠y,存在z∈{y+λη(x,y):λ∈(0,1)},使得η(x,y)Tf(z)≠0,则称f为集合K上相对于η的严格不变拟单调映射。并建立了严格不变拟单调与严格预拟不变凸之间的关系:设K为Rn中的不变凸集,f是K上的可微函数,η:Rn×Rn→Rn,如果η满足文中所述条件1,则f是集合K上相对于η的严格预拟不变凸函数的充分必要条件是f是集合K上相对于η的严格不变拟单调,且对所有x,y∈K,有f(y)≤f(x)f(y+η(x,y))≤f(x)成立。
In this paper, the strictly invariant quasimonotone is defined as an extension of strictly quasimonotone ： Let K of R^n be an invex set with respect to η：R^n×R^n→R^n. A mapfis strictly invariant quasimonotone with respect to the same η on K, iffis invariant quasimonotone, and for any distinct x,y ∈ K, there exists z∈{y＋λη（x,y）：λ∈（0,1）}, such as η（x,y）^T F（z）≠0. Relationship between strictly invariant quasimonotonicity and strictly prequasiinvexity are established ： Let K of R^n be an invex set with respect to η, and let f be a differentiable function on K. If η satisfies condition 1, then f is strictly prequasiinvex with respect to the same η on K, if and only if △↓f is strictly invariant quasimonotone with respect to the same η on K, and for all x,y ∈ K,f（y） ≤f（x） implies f（y ＋ η（x,y） ） ≤f（x）.
出处
《重庆师范大学学报（自然科学版）》
CAS
2005年第3期60-62,共3页
Journal of Chongqing Normal University:Natural Science
关键词
严格不变拟单调
严格预拟不变凸
等价关系
strictly invariant quasimonotone
strictly prequasiinvex
equivalent relation
