The Complexity of Computing KKT Solutions of Quadratic Programs

John Fearnley; Paul W. Goldberg; Alexandros Hollender; Rahul Savani

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arXiv · 2311.13738

The Complexity of Computing KKT Solutions of Quadratic Programs

John Fearnley·Paul W. Goldberg·Alexandros Hollender·Rahul Savani

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

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John Fearnley, Paul W. Goldberg, Alexandros Hollender, Rahul Savani. 2023-11-22. The Complexity of Computing KKT Solutions of Quadratic Programs. https://arxiv.org/abs/2311.13738

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