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Multiple-gradient descent algorithm (MGDA) for multiobjective optimization. (English. Abridged French version) Zbl 1241.65057
Summary: One considers the context of the concurrent optimization of several criteria \(J_{i}(Y) (i=1,\ldots ,n)\), supposed to be smooth functions of the design vector \(Y\in \mathbb R^{N} (n\leqslant N)\). 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.

MSC:
65K05 Numerical mathematical programming methods
90C29 Multi-objective and goal programming
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