A Descent Lemma Beyond Lipschitz Gradient Continuity: First-Order Methods Revisited and Applications

@article{Bauschke2017ADL,
  title={A Descent Lemma Beyond Lipschitz Gradient Continuity: First-Order Methods Revisited and Applications},
  author={Heinz H. Bauschke and J. Bolte and M. Teboulle},
  journal={Math. Oper. Res.},
  year={2017},
  volume={42},
  pages={330-348}
}
The proximal gradient and its variants is one of the most attractive first-order algorithm for minimizing the sum of two convex functions, with one being nonsmooth. However, it requires the differentiable part of the objective to have a Lipschitz continuous gradient, thus precluding its use in many applications. In this paper we introduce a framework which allows to circumvent the intricate question of Lipschitz continuity of gradients by using an elegant and easy to check convexity condition… Expand
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