The paper considers robust parametric optimization problems using multipoint formulations and makes the link with momentum-based formulations. Optimal sampling issues are discussed, and a procedure is proposed to quantify the confidence level on the robustness of the design. We also discuss incomplete sensitivity evaluations to take into account the computational complexity constraint. This permits to take advantage of what was previously developed for efficient monopoint design where the cost of the optimization is comparable with one state evaluations. The proposed algorithm is fully parallel and the time-to-solution is comparable with monopoint situations. Concepts are introduced through simple examples, and the paper ends with the design of the shape of an aircraft robust over a range of transverse winds.Copyright © 2013 John Wiley & Sons, Ltd.