Optimizing various modern components often involves solving complex problems governed by suitably-defined Partial Differential Equations (PDEs). The computational demands of solving these PDEs multiple times can make the overall optimization procedure cost can quickly become prohibitively expensive. Gradient based optimization, coupled with adjoint techniques, has proven to yield powerful and efficient algorithms. Yet, in some cases, even adjoint-based optimization can demonstrate a rather slow convergence rate. On that account, this study proposes a novel one-shot approach based on a full-space Newton solver. In contrast to the conventional adjoint-based optimization where one fully converges one equation at a time, in one-shot approach the PDEs are solved simultaneously with the optimization problem in a coupled iteration step. Central element of our method is the Karush–Kuhn–Tucker (KKT) linear system, where we employ an exact Newton method that exhibits a quadratic convergence rate towards the optimum. We test our method on the inverse design of a quasi 1-D de Laval nozzle, where the objective is to achieve a target pressure distribution across the nozzle. This simplified test case serves as an initial proof of concept for our method, laying the groundwork for the development of the general 3-D approach within in-house optimizer CADO.