Abstract

We study the local and global versions of the convexity, which is closely related to the problem of extending a convex function on a non-convex domain to a convex function on the convex hull of the domain and beyond the convex hull. We also give the parallel results for the convexity defined by positive definite Hessian.

Author information

Contact details are reproduced from the original publication and may be historical.

Min Yan

Dept. of Mathematics, University of Science and Technology, Clear Water Bay, Hong Kong

mamyan@ust.hk

Keywords

  • Convex function
  • non-convex domain
  • convex hull
  • positive definite Hessian
  • extension

Mathematics Subject Classification

26B25

Suggested citation

M. Yan. “Extension of Convex Function.” Journal of Convex Analysis 21 (2014), No. 4, 965–987. https://doi.org/10.68381/jca21052

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Published by Heldermann Verlag, 2014. Rights now held by Banach Press.