Nonlinear residual minimization by iteratively reweighted least squares

@article{Sigl2016NonlinearRM,
  title={Nonlinear residual minimization by iteratively reweighted least squares},
  author={Juliane Sigl},
  journal={Computational Optimization and Applications},
  year={2016},
  volume={64},
  pages={755-792}
}
  • Juliane Sigl
  • Published 26 April 2015
  • Mathematics, Computer Science
  • Computational Optimization and Applications
In this paper we address the numerical solution of minimal norm residuals of nonlinear equations in finite dimensions. We take particularly inspiration from the problem of finding a sparse vector solution of phase retrieval problems by using greedy algorithms based on iterative residual minimizations in the $$\ell _p$$ℓp-norm, for $$1 \le p \le 2$$1≤p≤2. Due to the mild smoothness of the problem, especially for $$p \rightarrow 1$$p→1, we develop and analyze a generalized version of iteratively… 
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