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.
On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators,
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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.