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hal-00694039, version 2

## Application of MGDA to domain partitioning

Jean-Antoine Désidéri (, ) 1

N° RR-7968 (2012)

Résumé : This report is a sequel to several publications in which a {\em Multiple-Gradient Descent Algorithm (MGDA)} has been proposed and tested for the treatment of multi-objective differentiable optimization. The method was originally introduced in \cite{JAD09:MGDA}, and again formalized in \cite{JAD12:MGDA-CRAS}. Its efficacy to identify the Pareto front has been demonstrated in \cite{JAD11:MGDA-PAES}, in comparison with an evolutionary strategy. Finally, recently, a variant, {\em MGDA II}, has been proposed in which the descent direction is calculated by a direct procedure \cite{JAD12:MGDA2}. In this new report, the efficiency of the algorithm is tested in the context of a simulation by domain partitioning, as a technique to match the different interface components concurrently. For this, the very simple testcase of the finite-difference discretization of the Dirichlet problem over a square is considered. The study aims at assessing the performance of {\em MGDA} in a discretized functional setting. One of the main teachings is the necessiy, here found imperative, to normalize the gradients appropriately.

• 1 :  OPALE (INRIA Sophia Antipolis / INRIA Grenoble Rhône-Alpes)
• INRIA – CNRS : UMR6621 – Université Nice Sophia Antipolis [UNS]
• Domaine : Mathématiques/Analyse numérique
• Mots-clés : multiobjective optimization – descent direction – convex hull – Gram-Schmidt orthogonalization process
• Référence interne : RR-7968
• Versions disponibles :  v1 (04-05-2012) v2 (21-05-2012)

• hal-00694039, version 2
• oai:hal.inria.fr:hal-00694039
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• Soumis le : Lundi 21 Mai 2012, 10:30:33
• Dernière modification le : Mardi 5 Juin 2012, 15:54:46