黎曼流形上非线性凸规划最优性条件的研究

计算机科学 ›› 2014, Vol. 41 ›› Issue (2): 95-98.

黎曼流形上非线性凸规划最优性条件的研究

邹丽,温欣,林彬

辽宁师范大学计算机与信息技术学院大连116081;辽宁师范大学计算机与信息技术学院大连116081;辽宁师范大学计算机与信息技术学院大连116081

出版日期:2018-11-14 发布日期:2018-11-14
基金资助:
本文受国家自然科学基金(61105059,5,61173100),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

Optimality Conditions on Riemannian Manifold of Nonlinear Convex Programming

ZOU Li,WEN Xin and LIN Bin

Online:2018-11-14 Published:2018-11-14

摘要/Abstract

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。

关键词: 黎曼流形,凸函数,最优性条件,广义梯度中图法分类号TP181文献标识码A

Abstract: This paper gave the identification of convex function on Riemannian manifold by use of Penot generalized directional 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.

Key words: Riemannian manifold,Convex function,Optimality condition,Generalized gradient

邹丽,温欣,林彬. 黎曼流形上非线性凸规划最优性条件的研究[J]. 计算机科学, 2014, 41(2): 95-98. https://doi.org/

ZOU Li,WEN Xin and LIN Bin. Optimality Conditions on Riemannian Manifold of Nonlinear Convex Programming[J]. Computer Science, 2014, 41(2): 95-98. https://doi.org/

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