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An adaptive accelerated first-order method for convex optimization

Renato D. C. Monteiro (monteiro***at***isye.gatech.edu)
Camilo Ortiz (camiort***at***gatech.edu)
Benar F. Svaiter (benar***at***impa.br)

Abstract: This paper presents a new accelerated variant of Nesterov's method for solving composite convex optimization problems in which certain acceleration parameters are adaptively (and aggressively) chosen so as to substantially improve its practical performance compared to existing accelerated variants while at the same time preserve the optimal iteration-complexity shared by these methods. Computational results are presented to demonstrate that the proposed adaptive accelerated method endowed with a restarting scheme outperforms other existing accelerated variants.

Keywords: complexity, accelerated gradient methods, convex optimization, conic optimization, quadratic programming

Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Category 2: Convex and Nonsmooth Optimization (Convex Optimization )


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Entry Submitted: 08/03/2012
Entry Accepted: 08/03/2012
Entry Last Modified: 05/28/2014

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