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The bound $ \epsilon $.

See Section 3.4.2 to know about $ \epsilon $.
If we have updated the value of $ M$ less than 10 times, we will set $ \epsilon:=0$ (see Section 3.4.1 to know about $ M$). This is because we are not sure of the value of $ M$ if it has been updated less than 10 times.
If the step size $ \Vert s^*\Vert$ we have computed at step 3 of the CONDOR algorithm is $ \displaystyle \Vert s^*\Vert \geq \frac{\rho}{2} $, then $ \epsilon=0$.
Otherwise, $ \epsilon= \frac{1}{2} \rho^2 \lambda_1$, where $ \lambda_1$ is an estimate of the slope of $ q(x)$ around $ \boldsymbol {x}_{(k)}$ (see Section 4.10 to know how to compute $ \lambda_1$).
We see that, when the slope is high, we permit a more approximative ($ =$ big value of $ \epsilon $) model of the function.

Frank Vanden Berghen 2004-04-19