Infeasible path optimal design methods with applications to aerodynamic shape optimization

We consider optimal design of physical systems described by a nonlinear boundary value problem. We propose a sequential quadratic programming method specifically tailored to the solution of this class of design problems. A particular representation of the null space of the constraint Jacobian that exploits its specific structure is employed. The resulting method avoids resolution of nonlinear behavior at the optimization iterations while keeping the size of the problem as small as that of conventional approaches. Three variants of the method are developed and discussed. These entail the solution of either two or three linear systems involving the Jacobian matrix of the discretized form of the boundary value problem. The method is used to solve aerodynamic design problems involving nonlinear transonic flow. No special provisions are made for treating discontinuities, and therefore the present implementation of the method is limited to problems with no shocks. Problems with up to 90 shape design variables are solved. Numerical results demonstrate a substantial performance improvement over conventional methods.