\begin{latin}
Solve the LP(5) with trust region \Delta _j^{LP} to obtain step d_j^{LP}, and \mathcal{W}^j.\\
Choose v_k;\, compute \lambda_k and H(x_k,\lambda_k).\\
If q_k(d_l^{LP})>q_k(0)-0.1[l_k(0)-l_k(d_l^{LP})]\,Then\\
\Delta _{j+1}^{LP}=\gamma^{dec} \Delta _j^{LP}
\end{latin}