Next: The parallel extension of Up: The CONDOR unconstrained algorithm. Previous: The bound . Contents

Note about the validity check.

When the computation for the current $\rho$ is complete, we check the model (see step 14 of the algorithm) around $\boldsymbol {x}_{(k)}$ , then one or both of the conditions:

$\displaystyle \Vert\boldsymbol{x}_{(j)}-\boldsymbol{x}_{(k)}\Vert \leq 2 \rho$

(6.5)

$\displaystyle \frac{1}{6}M \Vert \boldsymbol{x}_{(j)}- \boldsymbol{x}_{(k)} \Ve... ...ert P_j(\boldsymbol{x}_{(k)}+d)\vert : \Vert d \Vert \leq \rho \} \leq \epsilon$

(6.6)

must hold for every points in the dataset. When $\rho$ is reduced by formula 6.4, the equation 6.5 is very often NOT verified. Only Equation 6.6, prevents the algorithm from sampling the model at

new points. Numerical experiments indicate that the algorithm is highly successful in that it computes less then $\frac{1}{2}n^2$ new points in most cases.

Frank Vanden Berghen 2004-04-19