Nonlinear mapping and distance geometry

@article{Franc2018NonlinearMA,
  title={Nonlinear mapping and distance geometry},
  author={Alain Franc and Pierre Blanchard and Olivier Coulaud},
  journal={Optimization Letters},
  year={2018},
  volume={14},
  pages={453-467}
}
Distance Geometry Problem (DGP) and Nonlinear Mapping (NLM) are two well established questions: DGP is about finding a Euclidean realization of an incomplete set of distances in a Euclidean space, whereas Nonlinear Mapping is a weighted Least Square Scaling (LSS) method. We show how all these methods (LSS, NLM, DGP) can be assembled in a common framework, being each identified as an instance of an optimization problem with a choice of a weight matrix. We study the continuity between the… 
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