A derivative-free Algorithm for Bound Constrained Optimization

In this work, we propose a new globally convergent derivative-free
algorithm for the minimization of a continuously differentiable function in
the case that some of (or all) the variables are bounded. This algorithm
investigates the local behaviour of the objective function on the feasible
set by following a pattern search along the coordinate directions.
Whenever a ``suitable" descent feasible coordinate direction is detected
a new point is produced by performing a linesearch along this direction.
The information progressively obtained during the iterates of the
algorithm can be used to build an approximation model of the objective
function.The minimum of such a model is accepted if it produces an
improvement of the objective function value. We also derive a bound for the
limit accuracy of the algorithm in the minimization of noisy functions.
Finally, we report the results of a preliminary numerical experience.