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On the acceleration of augmented Lagrangian method for linearly constrained optimization

Bingsheng He(hebma***at***nju.edu.cn)
Xiaoming Yuan(xmyuan***at***hkbu.edu.hk)

Abstract: The classical augmented Lagrangian method (ALM) plays a fundamental role in algorithmic development of constrained optimization. In this paper, we mainly show that Nesterov's influential acceleration techniques can be applied to accelerate ALM, thus yielding an accelerated ALM whose iteration-complexity is O(1/k^2) for linearly constrained convex programming. As a by-product, we also show easily that the convergence rate of the original ALM is O(1/k).

Keywords: Convex programming, augmented Lagrangian method, acceleration

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )


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Entry Submitted: 10/11/2010
Entry Accepted: 10/11/2010
Entry Last Modified: 10/11/2010

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