The Complexity of Computing KKT Solutions of Quadratic Programs
Computational Complexity
2025-07-30 v2 Optimization and Control
Abstract
It is well known that solving a (non-convex) quadratic program is NP-hard. We show that the problem remains hard even if we are only looking for a Karush-Kuhn-Tucker (KKT) point, instead of a global optimum. Namely, we prove that computing a KKT point of a quadratic polynomial over the domain is complete for the class CLS = PPADPLS.
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Cite
@article{arxiv.2311.13738,
title = {The Complexity of Computing KKT Solutions of Quadratic Programs},
author = {John Fearnley and Paul W. Goldberg and Alexandros Hollender and Rahul Savani},
journal= {arXiv preprint arXiv:2311.13738},
year = {2025}
}
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