黎曼流形上的广义向量似变分不等式和向量优化问题  

Generalized Vector Variational-like Inequality and Vector Optimization Problem on Riemannian Manifolds

作　　者：陈胜兰[1] 方长杰[1] 

机构地区：[1]重庆邮电大学理学院,重庆400065

出　　处：《四川师范大学学报（自然科学版）》2016年第3期332-336,共5页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(11426055);重庆市教委科研项目(KJ070514)

摘　　要：利用黎曼流形上广义次微分的概念,定义Minty型和Stampcchia型的广义(弱)向量似变分不等式,并在不变凸性的假设下建立向量优化问题与广义弱向量似变分不等式的等价关系.方法和结果是新的,且推广了这一领域内许多已知结果.In this paper,we introduce a Minty type vector variational inequality,a Stampacchia type vector variational inequality,and the weak forms of them,which are all defined by means of generalized subdifferentials on Riemannian manifolds. We also establish a relationship between generalized vector variational-like inequalities and nonsmooth vector optimization problems on Riemannian manifolds under the assumption of invexity or invariant monotonicity. Our approach and results are new and generalize many known results in this field.

关 键 词：黎曼流形 广义向量似变分不等式 不变凸函数 向量优化 

分 类 号：O186.12[理学—数学] O224[理学—基础数学]