The Identification of Convex Function on Riemannian Manifold

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...

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Bibliographic Details
Published in:Mathematical problems in engineering 2014-01, Vol.2014 (2014), p.1-6
Main Authors: Shi, Yan, Karimi, Hamid Reza, Wen, Xin, Zou, Li
Format: Article
Language:English
Subjects:
Brownian motion
Convexity
Derivatives
Functions (mathematics)
Inequalities
Manifolds
Mathematical analysis
Mathematical programming
Nonlinearity
Optimization
Programming
Proving
Riemann manifold
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Summary: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.
ISSN:1024-123X
1563-5147
DOI:10.1155/2014/273514