A new approach to three-dimensional design of turbomachinery blades is presented. A number of heuristic and gradient based optimisers are used in conjunction with a linear sensitivity analysis tool, FAITH, to re-design a turbine nozzle guide vane. A novel linear approach is used to eliminate the large computational costs usually associated with function evaluations which are essentially solutions to the Navier-Stokes equations. Results are compared with those obtained previously from the inverse design mode of FAITH. With the present approach, it is shown that nonlinear complicated cost functions can be reduced significantly and aerodynamic and geometrical constraints can be handled easily and efficiently.