An economic non-linear minimization algorithm for bound constraint

In this paper, a steepest descent projection type algorithm for minimizing a general non-linear differentiable function under simple bound constraints is proposed. This kind of problem appears either in the direct resolution of simple optimization models in engineering, or in the indirect resolution of more complex optimization models by means of the resolution of a sequence of simpler models. More generally the proposed algorithm is, at least conceptually, applicable to the minimization of a non-linear differentiable function over any convex compact set. Thus the algorithm and its main convergence result are developed in this more general setting. Then the algorithm is specialized to the case of simple bound constraints. As a consequence, the reader interested mainly in applying the algorithm to this last case may simply skip the convergence result given for the more general case.