Gradient-Based, Post-Optimality Sensitivity Analysis with Respect to Parameters of State Equations

Design optimization is a computational tool that can enable a designer to investigate the effectiveness of a design concept in an organized format. However, this design process requires the design variables, constraints, and objective function to be properly defined and expressed in mathematical forms. Post-optimality analysis thus becomes a necessary step to investigate different variations in the problem formulation and parameters to ensure that optimization produces a stable and trustworthy outcome. One efficient way to achieve this aim is to compute the local derivative of the optimized objective function with respect to the optimization problem parameters, such as bounds on the constraints and the material properties in the state equation. This method is referred to as post-optimality sensitivity analysis. In this study, we derived the post-optimal sensitivity equation to explicitly include the derivatives of state variables with respect to problem parameters and to broaden its applications to minimax and goal attainment design optimization problems.