Solving Most Systems of Random Quadratic Equations

@inproceedings{Wang2017SolvingMS,
  title={Solving Most Systems of Random Quadratic Equations},
  author={Gang Wang and Georgios B. Giannakis and Yousef Saad and Jie Chen},
  booktitle={NIPS},
  year={2017}
}
This paper deals with finding an n-dimensional solution x to a system of quadratic equations yi = |〈ai,x〉|, 1 ≤ i ≤ m, which in general is known to be NP-hard. We put forth a novel procedure, that starts with a weighted maximal correlation initialization obtainable with a few power iterations, followed by successive refinements based on iteratively reweighted gradient-type iterations. The novel techniques distinguish themselves from prior works by the inclusion of a fresh (re)weighting… CONTINUE READING