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

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.