Nonconvex Quadratic System | Computational Neuroscience and Artificial Intelligence Lab

1. Global Convergence of Nonconvex Quadratic Systems

A basin of attraction exists around the global optimum of a nonconvex quadratic system (Huang et al., 2020). When the initialization is inside the basin of attraction, the gradient descent updates converge linearly toward the global optimum.

2. Reconstructing Point Sets from Distance Distributions

A set of points on a line or a loop is reconstructed from their unlabelled pairwise distances via a nonconvex quadratic formulation (Huang & Dokmanić, 2021).

A DNA sequence (line) with 5 segmentation sites is reconstructed from its random segments.

References

2021

TSP

Reconstructing Point Sets From Distance Distributions

Shuai Huang, and Ivan Dokmanić

IEEE Transactions on Signal Processing, 2021

Bib HTML

@article{uDGP_1D,
  author = {Huang, Shuai and Dokmani\'{c}, Ivan},
  journal = {IEEE Transactions on Signal Processing},
  title = {Reconstructing Point Sets From Distance Distributions},
  year = {2021},
  volume = {69},
  number = {},
  pages = {1811-1827}
}

2020

TSP

Solving Complex Quadratic Systems With Full-Rank Random Matrices

Shuai Huang, Sidharth Gupta, and Ivan Dokmanić

IEEE Transactions on Signal Processing, 2020

Bib HTML

@article{nonconvex_quadratic,
  author = {Huang, Shuai and Gupta, Sidharth and Dokmani\'{c}, Ivan},
  journal = {IEEE Transactions on Signal Processing},
  title = {Solving Complex Quadratic Systems With Full-Rank Random Matrices},
  year = {2020},
  volume = {68},
  number = {},
  pages = {4782-4796}
}