On the complexity of finding a local minimizer of a quadratic function over a polytope

@article{Ahmadi2022OnTC,
  title={On the complexity of finding a local minimizer of a quadratic function over a polytope},
  author={Amir Ali Ahmadi and Jeffrey O. Zhang},
  journal={Mathematical Programming},
  year={2022},
  pages={1-10}
}
We show that unless P=NP, there cannot be a polynomial-time algorithm that finds a point within Euclidean distance $$c^n$$ c n (for any constant $$c \ge 0$$ c ≥ 0 ) of a local minimizer of an n -variate quadratic function over a polytope. This result (even with $$c=0$$ c = 0 ) answers a question of Pardalos and Vavasis that appeared in 1992 on a list of seven open problems in complexity theory for numerical optimization. Our proof technique also implies that the problem of deciding whether a… 

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