Multiple-gradient descent algorithm (MGDA) for multiobjective optimization

摘要

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.