We present new insights into how to achieve higher frequencies in large-scale nonlinear predictive control using truncated-like schemes. The basic idea is that, instead of solving the full nonlinear programming (NLP) problem at each sampling time, we solve a single, truncated quadratic programming (QP) problem. We present conditions guaranteeing stability of the approximation error derived through this type of scheme using generalized equation concepts. In addition, we propose a preliminary scheme using an augmented Lagrangian reformulation of the NLP and projected successive over relaxation to solve the underlying QP. This strategy enables early termination of the QP solution because it can perform linear algebra and active-set identification tasks simultaneously. A simple numerical case study is used to illustrate the developments.