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.
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)
出处
《应用数学和力学》
CSCD
北大核心
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)。