Adaptive Multiscale Methods for the Solution of Dynamic Optimization Problems

Abstract:
Dynamic optimization is a distinguished method capable of improving process operaiton. Unfortunately, dynamic optimization problems can become quite expensive to solve. Besides, in on-line optimization a solution has to be prompted within a fixed response time such that the solution method has to be real-time capable. Flexible and scalable solution methods, which use as much time as available and successively improve the solution, are natural candidates for real-time capable algorithms. This thesis suggests and analyses a multiscale methodology to solve dynamic optimization problems in a flexible and scalable manner. The proposed methodology constructs a hierarchy of successively, adaptively refined problems and aims to lower the numerical cost needed to solve the dynamic optimization problem. Furthermore, the methodology is capable to regularize the ill-posed problems. Wavelets and local single scale functions are used to realize the concept and the consequences with respect to real-time capability and numerical cost are thoroughly discussed using several examples.

Keywords:
Dynamic optimization, on-line optimization, real-time optimization, adaptive refinement, nested iteration, inverse problems, regularization, Wavelets, multiscale approximation, hierarchical basis functions.