摘要
在黎曼流形上分别给出广义方向导数、广义梯度、不变凸变集和不变凸函数等概念,定义两类似变分不等式,分别讨论这两类变分不等式与向量优化问题有效解之间的关系.
The definitions of generalized directional derivative, generalized gradient, invex set and invex function definned on Riemannian manifolds were presented respectively. The relationships between invex function and quasi-invex function, as well as pseudo-invex function were given. The concepts of (weak) vector variational inequality were given. Moreover, with the conditions of invex or geodesic convex function, the relationships between the solutions of (weak) vector variational inequalities and the (weak) efficient solutions of vectoroptimizations were studied.
出处
《安徽大学学报(自然科学版)》
CAS
北大核心
2009年第3期5-8,共4页
Journal of Anhui University(Natural Science Edition)
基金
国家自然科学基金资助项目(60574075)
关键词
向量变分不等式
向量优化
有效解
不变凸函数
黎曼流形
vector variational inequality
vector optimization
efficient solution
invex function
Riemannian manifold