Year: 2026
Type: preprint
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 $\ell_k$-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.
Source: arXiv (Cornell University)
Authors: Schwan, Roland, Lew, Thomas, Plancher, Brian
Institutions: Dartmouth College, Toyota Research Institute
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223885391