Convergence of first-order methods via the convex conjugate

  • Javier F. Peña
    • Categories Convex Optimization Tags , Short URL: https://optimization-online.org/?p=14692

    This paper gives a unified and succinct approach to the $O(1/\sqrt{k}), O(1/k),$ and $O(1/k^2)$ convergence rates of the subgradient, gradient, and accelerated gradient methods for unconstrained convex minimization. In the three cases the proof of convergence follows from a generic bound defined by the convex conjugate of the objective function.

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    Working Paper, Carnegie Mellon University

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