On se place dans le contexte de lʼoptimisation concourante de plusieurs critères (), fonctions régulières du vecteur de conception (). On donne une solution constructive originale au problème de lʼidentification dʼune direction de descente commune à tous les critères en un point non optimal au sens de Pareto. On est conduit à généraliser la méthode classique du gradient au contexte multiobjectif en utilisant cette direction pour la descente. On prouve que lʼalgorithme converge alors vers un point de conception Pareto-stationnaire.
One considers the context of the concurrent optimization of several criteria (), supposed to be smooth functions of the design vector (). An original constructive solution is given to the problem of identifying a descent direction common to all criteria when the current design-point 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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@article{CRMATH_2012__350_5-6_313_0, author = {D\'esid\'eri, Jean-Antoine}, title = {Multiple-gradient descent algorithm {(MGDA)} for multiobjective optimization}, journal = {Comptes Rendus. Math\'ematique}, pages = {313--318}, publisher = {Elsevier}, volume = {350}, number = {5-6}, year = {2012}, doi = {10.1016/j.crma.2012.03.014}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2012.03.014/} }
TY - JOUR AU - Désidéri, Jean-Antoine TI - Multiple-gradient descent algorithm (MGDA) for multiobjective optimization JO - Comptes Rendus. Mathématique PY - 2012 SP - 313 EP - 318 VL - 350 IS - 5-6 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2012.03.014/ DO - 10.1016/j.crma.2012.03.014 LA - en ID - CRMATH_2012__350_5-6_313_0 ER -
%0 Journal Article %A Désidéri, Jean-Antoine %T Multiple-gradient descent algorithm (MGDA) for multiobjective optimization %J Comptes Rendus. Mathématique %D 2012 %P 313-318 %V 350 %N 5-6 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2012.03.014/ %R 10.1016/j.crma.2012.03.014 %G en %F CRMATH_2012__350_5-6_313_0
Désidéri, Jean-Antoine. Multiple-gradient descent algorithm (MGDA) for multiobjective optimization. Comptes Rendus. Mathématique, Tome 350 (2012) no. 5-6, pp. 313-318. doi : 10.1016/j.crma.2012.03.014. http://archive.numdam.org/articles/10.1016/j.crma.2012.03.014/
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