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The Identification of Convex Function on Riemannian Manifold

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  • Li Zou
  • Xin Wen
  • Hamid Reza Karimi
  • Yan Shi

Abstract

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.

Suggested Citation

  • Li Zou & Xin Wen & Hamid Reza Karimi & Yan Shi, 2014. "The Identification of Convex Function on Riemannian Manifold," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-6, April.
    • Handle: RePEc:hin:jnlmpe:273514
    DOI: 10.1155/2014/273514
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