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Integration Methods and Accelerated Optimization Algorithms

Damien Scieur(damien.scieur***at***inria.fr)
Vincent Roulet(vincent.roulet***at***inria.fr)
Francis Bach(francis.bach***at***inria.fr)
Alexandre d'Aspremont(aspremon***at***ens.fr)

Abstract: We show that accelerated optimization methods can be seen as particular instances of multi-step integration schemes from numerical analysis, applied to the gradient flow equation. In comparison with recent advances in this vein, the differential equation considered here is the basic gradient flow and we show that multi-step schemes allow integration of this differential equation using larger step sizes, thus intuitively explaining acceleration results.


Category 1: Convex and Nonsmooth Optimization (Convex Optimization )


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Entry Submitted: 05/30/2017
Entry Accepted: 05/30/2017
Entry Last Modified: 05/30/2017

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