This paper presents a new strategy of simplifying the online computations in linear model predictive control (MPC). Employing a specific type of state dependent parameterization for the optimization variable in MPC, advantages of explicit MPC are combined with those of online optimization based MPC into an efficient MPC scheme. The parameterization is computed offline applying a tailored subspace clustering algorithm to training data consisting of states and corresponding solutions to the MPC optimization problem. It is then refined to guarantee feasibility of the parameterized optimization. During the offline design phase, complexity of the parameterization can be adjusted and control performance can be traded off against online computational effort and storage requirements. Numerical examples evaluate the presented methods and illustrate their benefits. (C) 2017 Elsevier Ltd. All rights reserved.