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Extension of Convex Function

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arxiv 1207.0944 v5 pith:DEQGQ5GD submitted 2012-07-04 math.CA math.DS

Min Yan This is my paper · ORCID
classification math.CAmath.DS
keywords convexfunctionconvexitydomainhullbeyondcloselydefined
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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.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Testing convexity of functions over finite domains

    cs.CC 2019-08 reject novelty 8.0 of 10

    Testing convexity on the line is tightly Θ(log(εn)/ε), with no adaptivity advantage, but the paper's adaptive stripe tester has a flaw that breaks the exponential separation as stated.

  2. Folded optimal transport and its application to separable quantum optimal transport

    math.FA 2025-12 conditional novelty 6.0 of 10

    Folded optimal transport builds a true Wasserstein distance on any compact convex set from a distance on its extreme points, giving separable quantum Wasserstein distances on density matrices and unifying classical, s...

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