黎曼流形上的向量似变分不等式与向量优化问题  

Vector variational-like inequalities and vector optimization problems on Riemannian manifolds

作　　者：肖刚[1] 肖红[1] 刘三阳[2] 

机构地区：[1]韩山师范学院数学与信息技术系,广东潮州521041 [2]西安电子科技大学理学院,陕西西安710071

出　　处：《安徽大学学报（自然科学版）》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)

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.

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 

分 类 号：O186[理学—数学]