cicyt UNIZAR
Full-text links:

Download:

Current browse context:

math.OC

Change to browse by:

References & Citations

Bookmark

(what is this?)
CiteULike logo BibSonomy logo Mendeley logo del.icio.us logo Digg logo Reddit logo ScienceWISE logo

Mathematics > Optimization and Control

Title: On the Fenchel Duality between Strong Convexity and Lipschitz Continuous Gradient

Authors: Xingyu Zhou
Abstract: We provide a simple proof for the Fenchel duality between strong convexity and Lipschitz continuous gradient. To this end, we first establish equivalent conditions of convexity for a general function that may not be differentiable. By utilizing these equivalent conditions, we can directly obtain equivalent conditions for strong convexity and Lipschitz continuous gradient. Based on these results, we can easily prove Fenchel duality. Beside this main result, we also identify several conditions that are implied by strong convexity or Lipschitz continuous gradient, but are not necessarily equivalent to them. This means that these conditions are more general than strong convexity or Lipschitz continuous gradient themselves.
Subjects: Optimization and Control (math.OC)
Cite as: arXiv:1803.06573 [math.OC]
  (or arXiv:1803.06573v1 [math.OC] for this version)

Submission history

From: Xingyu Zhou [view email]
[v1] Sat, 17 Mar 2018 21:29:20 GMT (6kb)