We propose a novel model predictive control (MPC) formulation, that ensures recursive feasibility, stability and performance under inexact dual optimization. Dual optimization algorithms offer a scalable solution and can thus be applied to large distributed systems. Due to constraints on communication or limited computational power, most real-time applications of MPC have to deal with inexact minimization. We propose a modified optimization problem inspired by robust MPC which offers theoretical guarantees despite inexact dual minimization. The approach is not tied to any particular optimization algorithm, but assumes that the feasible optimization problem can be solved with a bounded suboptimality and constraint violation. In combination with a distributed dual gradient method, we obtain a priori upper bounds on the number of required online iterations. The design and practicality of this method are demonstrated with a benchmark numerical example. (C) 2019 Elsevier Ltd. All rights reserved.