= Trust-region acceptance ratio
{title2=$\rho_k=\frac{f(x_k)-f(x_k+s_k)}{m_k(0)-m_k(s_k)}$}
For positive predicted decrease, the <trust-region acceptance ratio> compares the actual decrease with the model decrease. A ratio near one supports the local model; a negative ratio means the trial increased the <objective function>. A typical algorithm rejects and shrinks the <trust region> when $\rho_k<\eta_1$, accepts it when $\rho_k\geq\eta_1$, and enlarges the radius after a very successful boundary step with $\rho_k>\eta_2$, where $0<\eta_1<\eta_2<1$.
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