PROJECT TITLE :

Optimal Parameter Selection for the Alternating Direction Method of Multipliers (ADMM): Quadratic Problems

ABSTRACT:

The alternating direction technique of multipliers (ADMM) has emerged as a robust technique for massive-scale structured optimization. Despite many recent results on the convergence properties of ADMM, a quantitative characterization of the impact of the algorithm parameters on the convergence times of the tactic is still lacking. During this paper we notice the optimal algorithm parameters that minimize the convergence factor of the ADMM iterates in the context of $ell_2 $-regularized minimization and constrained quadratic programming. Numerical examples show that our parameter selection rules significantly outperform existing alternatives in the literature.


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