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PreprintarXiv licencearXiv

Efficient ADMM for Soft-Constrained Quadratic Programs via Generalized Slack Projections

  • Roland Schwan
  • Thomas Lew
  • Brian Plancher
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Abstract

Quadratic programs (QPs) are a core building block in many applications. In practice, constraints are often softened with slack variables to guarantee feasibility. The standard approach tackles this by introducing additional decision variables, growing the resulting optimization problem. In this paper, we propose an Alternating Direction Method of Multipliers (ADMM) scheme for a broad class of convex slack penalty functions, including all ℓk-norms, without increasing the problem size. The only change to the ADMM scheme is a modified slack projection function, while the remaining algorithm stays the same. We demonstrate our approach on numerical examples, showing significant speedups, and show its flexibility on an energy optimization problem.

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Cite

BibTeXRIS
BibTeX
@misc{schwan2026efficient,
  title = {{Efficient ADMM for Soft-Constrained Quadratic Programs via Generalized Slack Projections}},
  author = {Roland Schwan and Thomas Lew and Brian Plancher},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.35631},
  eprint = {2610.35631},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.35631},
}
RIS
TY  - UNPB
TI  - Efficient ADMM for Soft-Constrained Quadratic Programs via Generalized Slack Projections
AU  - Roland Schwan
AU  - Thomas Lew
AU  - Brian Plancher
PY  - 2026
DA  - 2026/10/26
PB  - arXiv
DO  - 10.48550/arxiv.2610.35631
UR  - https://arxiv.org/abs/2610.35631
AB  - Quadratic programs (QPs) are a core building block in many applications. In practice, constraints are often softened with slack variables to guarantee feasibility. The standard approach tackles this by introducing additional decision variables, growing the resulting optimization problem. In this paper, we propose an Alternating Direction Method of Multipliers (ADMM) scheme for a broad class of convex slack penalty functions, including all ℓ_k-norms, without increasing the problem size. The only change to the ADMM scheme is a modified slack projection function, while the remaining algorithm stays the same. We demonstrate our approach on numerical examples, showing significant speedups, and show its flexibility on an energy optimization problem.
ER  -