Riemann流形上ρ-(η,d)-B不变凸的向量变分不等式及向量优化问题  

Vector Variational-Like Inequalities and Vector Optimization Problems Involvingρ-(η,d)-B Invexity on Riemannian Manifolds

作　　者：刘爽 莫定勇 周志昂 LIU Shuang;MO Dingyong;ZHOU Zhiang(College of Science,Chongqing University of Technology,Chongqing 400054,P.R.China;Chongqing Yuzhong Insitute for Teacher Education,Chongqing 400015,P.R.China)

机构地区：[1]重庆理工大学理学院,重庆400054 [2]重庆市渝中区教师进修学院,重庆400015

出　　处：《应用数学和力学》2020年第4期458-466,共9页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11861002);重庆市基础与前沿研究计划项目(cstc2017jcyjBX0055,cstc2015jcyjBX0113)。

摘　　要：该文研究了Riemann流形上的优化问题.首先,利用广义方向导数在Riemann流形上引入ρ-(η,d)-B不变凸函数、ρ-(η,d)-B伪不变凸函数和ρ-(η,d)-B拟不变凸函数.其次,讨论了变分不等式的解与Riemann流形上向量优化问题解之间的关系.最后,建立了优化问题的Kuhn-Tucker充分条件.A class of optimality problems involving the generalized directional derivatives were studied on Riemannian manifolds.Firstly,by means of the generalized directional derivative,three concepts of theρ-(η,d)-B invex function,the pseudoρ-(η,d)-B invex function and the quasiρ-(η,d)-B invex function on Riemannian manifolds were introduced.Secondly,the relations between the solution to variational inequalities and the solution to the optimization problem on Riemannian manifolds were discussed.Finally,the Kuhn-Tucker sufficient condition for the optimality problem was established.

关 键 词：RIEMANN流形 向量变分不等式 向量优化问题 ρ-(η d)-B不变凸函数 

分 类 号：O221.6[理学—运筹学与控制论]