# 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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