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Mathematical Problems in Engineering
Volume 2014, Article ID 273514, 6 pages
Research Article

The Identification of Convex Function on Riemannian Manifold

1School of Computer and Information Technology, Liaoning Normal University, Dalian 116081, China
2State Key Laboratory for Novel Software Technology, Nanjing University, Nanjing 210093, China
3Department of Engineering, Faculty of Engineering and Science, University of Agder, Grimstad, Norway
4General Education Center (Kumamoto/Aso), Tokai University, Kumamoto, Japan

Received 30 December 2013; Accepted 26 February 2014; Published 7 April 2014

Academic Editor: Yuxin Zhao

Copyright © 2014 Li Zou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The necessary and sufficient condition of convex function is significant in nonlinear convex programming. This paper presents the identification of convex function on Riemannian manifold by use of Penot generalized directional derivative and the Clarke generalized gradient. This paper also presents a method for judging whether a point is the global minimum point in the inequality constraints. Our objective here is to extend the content and proof the necessary and sufficient condition of convex function to Riemannian manifolds.