Self-concordance is NP-hard

@article{Lim2017SelfconcordanceIN,
  title={Self-concordance is NP-hard},
  author={Lek-Heng Lim},
  journal={Journal of Global Optimization},
  year={2017},
  volume={68},
  pages={357-366}
}
  • Lek-Heng Lim
  • Published 29 March 2013
  • Economics
  • Journal of Global Optimization
We show that deciding whether a convex function is self-concordant is in general an intractable problem. 

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People have convinced me that I should use reducibility in Cook's sense as opposed to Karp's in the definition of NP-hard, and I think I have found a decent way to avoid the dile~mna between Cook's "Turing reducibilities" and Karp’s "many-one reducibles".