摘要
利用黎曼流形上Lipschitz函数的Penot广义方向导数和Clarke广义梯度,得到了黎曼流形上凸函数的判别,并得到了黎曼流形上凸规划极小点的充分条件,给出了黎曼流形上的等式约束优化问题、不等式约束优化问题及带有等式和不等式约束的优化问题的Lagrange定理、Lagrange充分条件、Kuhn-Tucker定理及极小点充分条件。
This paper gave the identification of convex function on Riemannian manifold by use of Penot generalized di-rectional derivative and the Clarke generalized gradient,and gave a sufficient condition for the minimum point of convex programming on Riemannian manifolds,and Lagrange theorem,Lagrange sufficient condition,the Kuhn-Tucker theorem and sufficient condition of the minimum point of the equality constrained optimization problems,the inequality constrained optimization problems,and equality and inequality constrained optimization problem was given.
作者
邹丽
温欣
林彬
ZOU Li;WEN Xin;LIN Bin(School of Computer Science and Information Technology,Liaoning Normal University,Dalian 116081,China;State Key Laboratory for Novel Software Technology,Nanjing University,Nanjing 210093,China)
出处
《计算机科学》
CSCD
北大核心
2014年第2期95-98,共4页
Computer Science
基金
国家自然科学基金(61105059,61175055,61173100)
国家自然科学基金国际(地区)合作与交流项目(61210306079)
中国博士后基金(2012M510815)
辽宁省杰出青年学者计划(LJQ2011116)资助
关键词
黎曼流形
凸函数
最优性条件
广义梯度
Riemannian manifold
Convex function
Optimality condition
Generalized gradient
