Preprint A115/2002
A projected gradient method for vector optimization problems

Alfredo Iusem | GraĆ±a Drummond, Luis Mauricio

**Keywords: **
Pareto optimality | weak efficiency | Projected gradient method

We consider extensions of the projected gradient method to vector optimization, which work directly with vector-valued functions, without using scalar-valued objectives. We provide a direction which adequately substitutes for the projected gradient, and establish results which mirror those available for the scalar-valued case, namely stationarity of the cluster points (if any) without convexity assumptions, and convergence of the full sequence generated by the algorithm to a weakly efficient optimum in the convex case, under mild assumptions. We also prove that our esults still hold when the search direction is only approximately computed.