English

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 [0,1]n[0,1]^n is complete for the class CLS = PPAD\capPLS.

Keywords

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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Journal version

R2 v1 2026-06-28T13:29:05.738Z