Sketch of the dogbox algorithm in two dimensions for step k. The previous point is x_k−i, the next point is x_k. The rectangle gives the trust region with size ∆, δ_gn is the Gauss–Newton step, and tδ_sd is the steepest decent step. Here the Gauss–Newton step falls outside the trust region, so the new step δ_k is a combination of the Gauss–Newton step and the steepest decent, cut off at the boundary of the trust region.