The link between linear model predictive control (MPC) and parametric linear/quadratic programming has reached maturity in terms of the characterization of the structural properties and the numerical methods available for the effective resolution. The computational complexity is one of the current bottlenecks for these control design methods and inverse optimality has been recently shown to provide a new perspective for this challenge. However, the question of the minimal complexity of inverse optimality formulation is still open and much under discussion. In this paper we revisit some recent results by pointing out unnecessary geometrical complications which can be avoided by the interpretation of the optimality conditions. Two algorithms for fine-tuning inverse optimality formulation will be proposed and the results will be interpreted via two illustrative examples in comparison with existing formulations.