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Convergence of first-order methods via the convex conjugate

Javier Pena(jfp***at***andrew.cmu.edu)

Abstract: 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.

Keywords: First-order methods, convex conjugate

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Citation: Working Paper, Carnegie Mellon University

Download: [PDF]

Entry Submitted: 07/27/2017
Entry Accepted: 07/27/2017
Entry Last Modified: 07/27/2017

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