Multiple-gradient descent algorithm (MGDA) for multiobjective optimization

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 is an element of R-N (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. (C) 2012 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.