FRANC, Alain; BLANCHARD, Pierre; COULAUD, Olivier

doi:10.1007/s11590-019-01431-y

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FRANC, Alain
Pleiade, from patterns to models in computational biodiversity and biotechnology [PLEIADE]
Biodiversité, Gènes & Communautés [BioGeCo]

BLANCHARD, Pierre
High-End Parallel Algorithms for Challenging Numerical Simulations [HiePACS]

COULAUD, Olivier
High-End Parallel Algorithms for Challenging Numerical Simulations [HiePACS]

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Optimization Letters. 2020, vol. 14, n° 2, p. 453-467

Springer Verlag

Résumé en anglais

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 solutions (which are point clouds) when the weight matrix varies, and the compactness of the set of solutions (after centering). We finally study a numerical example, showing that solving the optimization problem is far from being simple and that the numerical solution for a given procedure may be trapped in a local minimum.< Réduire

Mots clés en anglais

Distance Geometry Problem

Nonlinear Mapping

Least Square Scaling

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Nonlinear mapping and distance geometry

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