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 ∈ 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.