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

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.