Optimización de hiperparámetros para un problema de control óptimo no convexo.

Abstract

This work is focused on the optimization of hyperparameters for a non-convex optimal control problem. Associated Parameters to an optimal control problem (e.g. Tickhonov parameters) generally have economic meaning in the optimization process. Therefore choose these parameters with an optimality criterion, and not arbitrarily or empirically, is relevant to obtain solutions "improved". For this reason, we propose a bilevel problem, for the optimization of the hyperparameters of a non-convex optimal control problem, for which we will study and determine its optimality conditions.

Once the bilevel problem has been set, we first work with the lower level problem, establishing a regularization through which a family of optimal control problems is obtained (depending on the regularization parameter) that approximates the original. Then, the first-order scaled optimality condition associated with the regularized problem is established.

These optimality conditions characterize the solutions of the lower level problem, which are used to transform the bilevel problem into a single level problem. Finally, we will determine SB-KKT that characterize the optimal value of the hyperparameters in a formal way.