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Local linear convergence of the alternating direction method of multipliers for quadratic programs. (English) Zbl 1285.90033

Summary: The Douglas-Rachford alternating direction method of multipliers (ADMM) has been widely used in various areas. The global convergence of ADMM is well known, while the research on its convergence rate is still in its infancy. In this paper, we show the local linear convergence rate of ADMM for a quadratic program which includes some important applications of ADMM as special cases.

MSC:

90C25 Convex programming
65K10 Numerical optimization and variational techniques
65J22 Numerical solution to inverse problems in abstract spaces
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