Abstract Strong geodesic convex function and strong monotone vector field of order m on Riemannian manifolds are established. A characterization of strong geodesic convex function of order m for the continuously differentiable functions is discussed. The relation between the solution of a new variational inequality problem and the strict minimizers of order m for a multiobjective programing problem is also established.

中文翻译：

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m阶强测地凸函数

摘要 建立了黎曼流形上的强测地凸函数和m阶强单调向量场。讨论了连续可微函数的 m 阶强测地凸函数的表征。还建立了新变分不等式问题的解与多目标规划问题的 m 阶严格最小化器之间的关系。