We are interested in optimal design of 3D complex geometries, such as radial turbomachines, in large control space. The calculation of the gradient of the cost function is a key point when a gradient based method is used. Finite difference method has a complexity proportional to the size of the control space and the adjoint method requires important extra coding. We propose to consider the incomplete sensitivities method for optimal design of radial turbomachinery blades. The central point of the paper is how to adapt some formulations in radial turbomachinery to the validity domain of incomplete sensitivities. Also, we discuss on how to improve the accuracy of incomplete sensitivities using reduced order models based on physical assumptions. Fine/Turbo flow solver is coupled with gradient based optimization algorithms based on CAD-connected frameworks. Newton methods together with incomplete expressions of gradients are used. The approach is validated through optimization of centrifugal pumps. Finally the results are considered and discussed.