Corpus ID: 119682415

On the Fenchel Duality between Strong Convexity and Lipschitz Continuous Gradient

@article{Zhou2018OnTF,
  title={On the Fenchel Duality between Strong Convexity and Lipschitz Continuous Gradient},
  author={Xingyu Zhou},
  journal={arXiv: Optimization and Control},
  year={2018}
}
  • Xingyu Zhou
  • Published 2018
  • Mathematics
  • arXiv: Optimization and Control
  • 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… CONTINUE READING
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