  In this paper, we focus on developing efficient sensitivity analysis methods
for a computationally expensive objective function $f(x)$ in the case that the
minimization of it has just been performed. Here "computationally expensive"
means that each of its evaluation takes significant amount of time, and
therefore our main goal to use a small number of function evaluations of $f(x)$
to further infer the sensitivity information of these different parameters.
Correspondingly, we consider the optimization procedure as an adaptive
experimental design and re-use its available function evaluations as the
initial design points to establish a surrogate model $s(x)$ (or called response
surface). The sensitivity analysis is performed on $s(x)$, which is an lieu of
$f(x)$. Furthermore, we propose a new local multivariate sensitivity measure,
for example, around the optimal solution, for high dimensional problems. Then a
corresponding "objective-oriented experimental design" is proposed in order to
make the generated surrogate $s(x)$ better suitable for the accurate
calculation of the proposed specific local sensitivity quantities. In addition,
we demonstrate the better performance of the Gaussian radial basis function
interpolator over Kriging in our cases, which are of relatively high
dimensionality and few experimental design points. Numerical experiments
demonstrate that the optimization procedure and the "objective-oriented
experimental design" behavior much better than the classical Latin Hypercube
Design. In addition, the performance of Kriging is not as good as Gaussian RBF,
especially in the case of high dimensional problems.
