1)  invex set
不变凸集
1.
To improve research on the generalized convex function,some new characteristics of the prequasi-invex function are figured out by means of the cographical set of function(E(f)=(x,α)∶x∈K,α∈R,f(x)αH)and η-invex set,and its two applications in the mathematical programming problem are proposed.
借助于η-不变凸集和函数的上图(E(f)={(x,α)∶x∈K,α∈R,f(x)≤α})得到了预不变拟凸函数的几个新的性质,然后还给出了预不变拟凸函数在数学规划问题中的两个重要应用,从而完善了对此类广义凸函数的研究。
2.
Minty(strong) weak vector variational-like inequality and Stampacchia(strong) weak vector variational-like inequality had the same solution in the case that a matrix-valued function defined on invex set was a continuous invariant pseudomonotone mapping.
讨论两类向量似变分不等式解的关系问题,指出当定义在不变凸集上的映射是不变伪单调连续时,Minty(强)弱向量似变分不等式的解和Stampacchia(强)弱向量似变分不等式的解相同。
3.
To improve research on the generalized convex function,some new characteristics of the prequasi-invex function are figured out by means of the cographical set of function(E(f)={(x,α):x∈K,α∈R,f(x)≤α})and-invex set,and its two applications in the mathematical programming problem are proposed.
首先给出例子说明了此类广义凸函数的存在性,然后利用强η-不变凸集和函数的上图(E(f)={(x,α):x∈K,α∈R,f(x)≤α})得到了强预不变凸函数的几个重要性质,并用另一方法给出它的一个判别定理的简化证明,最后还给出了强预不变凸函数在数学规划问题中的一个重要应用,从而完善了对此类广义凸函数的研究。
2)  invex set
invex集
3)  invex set
invex set
4)  locally Hp-invex set
局部Hp-不变凸集
1.
This paper introduces new types of generalized convex functions and sets which are called locally(Hp,r,α)-preinvex functions and locally Hp-invex sets,respectively.
该文引进一类覆盖范围更为广泛的广义凸性概念(局部Hp-不变凸集,局部(Hp,r,α)-不变凸函数,局部(Hp,r,α)-拟凸),并讨论了这些凸性之间的相互关系。
5)  semi p-invex set
半p-不变凸集
1.
First,a class of generalized convex set called semi p-invex set is defined and based on this,by using semi-preinvexity functions and (p,r)-preinvexity functions,a class of new generalized convex functions called semi(p,r)-(pre)invexity functions are defined.
首先,定义了一类广义凸集——半p-不变凸集,在此基础之上,利用半预不变凸函数和(p,r)-预不变凸函数,定义了一类新的广义凸函数——半(p,r)-(预)不变凸函数,并举例说明了它既是半预不变凸函数又是(p,r)-预不变凸函数的真推广,从而是熟知的凸函数和不变凸函数的推广形式。
2.
First, a class of generalized convex set——semi p-invex set is defined and based on this,by using semi-preinvexity functions and (p,r)-preinvexity functions, a class of new generalized convex functions called semi (p,r)-preinvexity functions are defined.
首先,定义了一类广义凸集——半p-不变凸集,在此基础之上,利用半预不变凸函数和(p,r)-预不变凸函数,定义了一类新的广义凸函数——半(p,r)-预不变凸函数,并举例说明了它既是半预不变凸函数又是(p,r)-预不变凸函数的真推广,从而是熟知的凸函数和不变凸函数的推广形式。
6)  locally invex set
局部不变凸集
1.
First,locally invex set is defined and based on it a class of new generalized convex function called semilocallyλ- subinvex function is defined.
首先引入了局部不变凸集的概念,在此基础之上,定义了一类新的广义凸函数一半局部λ-次不变凸函数。
参考词条
补充资料：凸凸
1.高出貌。
说明：补充资料仅用于学习参考，请勿用于其它任何用途。