Journal of Convex Analysis 21 (2014), No. 4, 965--987
Copyright Heldermann Verlag 2014
Extension of Convex Function
Min Yan
Dept. of Mathematics, University of Science and Technology, Clear Water Bay, Hong Kong
mamyan@ust.hk
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.
Keywords: Convex function, non-convex domain, convex hull, positive definite Hessian, extension.
MSC: 26B25
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