摘要
针对黎曼流形上的非可微数学规划问题,在黎曼流形上分别给出了Lipschitz函数的广义方向导数和广义梯度的概念.利用黎曼流形局部与欧氏空间开集微分同胚的性质,把定义在线性空间上的广义方向导数和广义梯度的性质和运算法则通过切映射传递到流形的切空间上去.在此基础上,利用Ekeland变分原理,推导出基于黎曼流形上具有等式和不等式约束的数学规划问题的必要最优性条件.
In order to solve the nondifferentiable mathematical programming on Riemannian manifolds, the definitions of generalized directional derivative and generalized gradient of Lipschitz functions defined on Riemannian manifold are presented, respectively. By using tangent mapping, some properties of generalized directional derivative and generalized gradient are given. Moreover, the necessary optimality conditions in mathematical programming problem with equality and inequality constraints of Lipschitz functions are derived with the help of Ekeland variational principle on Riemannian manifolds.
出处
《东北师大学报（自然科学版）》
CAS
CSCD
北大核心
2009年第3期5-9,共5页
Journal of Northeast Normal University(Natural Science Edition)
基金
国家自然科学基金资助项目(60574075)
关键词
广义方向导数
广义梯度
必要最优性条件
黎曼流形
generalized directional derivative
generalized gradient
necessary optimality condition
riemannian manifold
