A systematic investigation of interior point methods for aerodynamic shape optimization

Abstract

We present an Interior-Point optimization framework for aerodynamic shape optimization, integrating the high-fidelity SU2 suite with IPOPT to handle high-dimensional, nonlinear design problems. The framework is evaluated using two standardized test cases from the AIAA Aerodynamic Design Optimization Discussion Group. The study systematically examines barrier parameter update strategies, including Mehrotra probing, the LOQO update rule, and quality function minimization, assessing their effectiveness in achieving convergence within non-convex design spaces. A KKT-error-based globalization approach is implemented to ensure stability and convergence to stationary points across different optimization scenarios. Results indicate that both heuristic and quality function-based update methods outperform the Fiacco-McCormick barrier parameter update strategy. However, the choice of update method is highly dependent on problem dimensionality: the quality function minimization approach performs favorably in low-dimensional design spaces, whereas heuristic methods exhibit superior convergence characteristics for higher-dimensional shape optimization problems. To further investigate the behavior of these strategies, gradient-based scaling methods—combined with heuristic and non-heuristic update techniques—are applied to a family of perturbed RAE 2822 airfoils and NASA Common Research Model wings. The results reveal the presence of multiple local optima within the design space, demonstrated by primal and dual residuals that confirm stationarity and feasibility at the converged solutions. While multiple local minima exist, we argue that the design space for both problems is relatively flat.