A modified projection in the ADMM z-update solves QPs with slack variables for feasibility without enlarging the original problem, and the method is proven equivalent to the standard expanded formulation.
Relaxed logarithmic barrier function based model predictive control of linear systems
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Solving Quadratic Programs with Slack Variables via ADMM without Increasing the Problem Size
A modified projection in the ADMM z-update solves QPs with slack variables for feasibility without enlarging the original problem, and the method is proven equivalent to the standard expanded formulation.