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Using a Factored Dual in Augmented Lagrangian Methods for Semidefinite Programming

Marianna De Santis (mdesantis***at***dis.uniroma1.it)
Franz Rendl (franz.rendl***at***aau.at)
Angelika Wiegele (angelika.wiegele***at***aau.at)

Abstract: In the context of augmented Lagrangian approaches for solving semidefinite programming problems, we investigate the possibility of eliminating the positive semidefinite constraint on the dual matrix by employing a factorization. Hints on how to deal with the resulting unconstrained maximization of the augmented Lagrangian are given. We further propose to use the approximate maximum of the augmented Lagrangian to improve the convergence rate of alternating direction augmented Lagrangian (ADAL) frameworks. Numerical results are shown, giving some insights on the benefits of the approach.

Keywords: Semidefinite Programming, Alternating Direction Augmented Lagrangian method, theta function

Category 1: Linear, Cone and Semidefinite Programming


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Entry Submitted: 10/13/2017
Entry Accepted: 10/13/2017
Entry Last Modified: 03/07/2018

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