Numerical Implementation of a Class of Infinite-Dimensional Primal-Dual Algorithms and Control Applications

This Thesis is devoted to primal-dual algorithms in the infinite-dimensional setting. We consider a class of infinite-dimensional optimization problems and its applications to optimal control problems. A primal-dual algorithm based on Nesterov-Todd direction is implemented. We apply this algorithm to two important control problems: multi-criteria linear-quadratic control problems and linear-quadratic control problems with quadratic constraints. Numerical experiments confirm very fast convergence of the algorithm which is predicted by the theory based on the concept of infinite-dimensional Jordan algebras. Necessary theoretical results have been developed. To the best of our knowledge this is the first implementation of this class of algorithms.