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Multiple-gradient descent algorithm (MGDA) for multiobjective optimization / Algorithme de descente à gradients multiples pour l'optimisation multiobjectif

Jean-Antoine Désidéri 1
1 OPALE - Optimization and control, numerical algorithms and integration of complex multidiscipline systems governed by PDE
CRISAM - Inria Sophia Antipolis - Méditerranée , JAD - Laboratoire Jean Alexandre Dieudonné : UMR6621
Abstract : One considers the context of the concurrent optimization of several criteria J i (Y ) (i = 1, . . . ,n), supposed to be smooth functions of the design vector Y ∈ RN (n N). An original constructive solution is given to the problem of identifying a descent direction common to all criteria when the current design-point Y^0 is not Pareto-optimal. This leads us to generalize the classical steepest-descent method to the multiobjective context by utilizing this direction for the descent. The algorithm is then proved to converge to a Pareto-stationary design-point.
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https://hal.inria.fr/hal-00768935
Contributor : Jean-Antoine Désidéri <>
Submitted on : Wednesday, December 26, 2012 - 5:37:49 PM
Last modification on : Monday, July 19, 2021 - 4:40:03 PM

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Jean-Antoine Désidéri. Multiple-gradient descent algorithm (MGDA) for multiobjective optimization / Algorithme de descente à gradients multiples pour l'optimisation multiobjectif. Comptes Rendus. Mathématique, Centre Mersenne (2020-..) ; Elsevier Masson (2002-2019), 2012, Tome 350 (Fascicule 5-6), pp.313-318. ⟨10.1016/j.crma.2012.03.014⟩. ⟨hal-00768935⟩

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