Inverse Parametric Optimization in a Set-Membership Error-in-Variables Framework

In this study, we aim to recover the interval hull of the set of feasible cost functions that can make uncertain observations optimal for a class of nonlinear constrained parametric optimization problems when all uncertainty and disturbances acting on observations or modeling are taken bounded but otherwise unknown. Fostering on inverse Karush-Kuhn-Tucker optimality conditions, we first state the solving equations as a constraint satisfaction problem, then show how to derive a safe overapproximation of the feasible solution set combining standard numerical tools and a posteriori validation with guaranteed methods based on interval analysis. The approach is evaluated on two well-tuned numerical examples: A discrete unicycle robot model and a planar elastica model, respectively.