Coupling the auxiliary problem principle with descent methods of pseudoconvex programming

The descent auxiliary problem method allows one to find the solution of minimization problems by solving a sequence of auxiliary problems which incorporate a linesearch strategy. We derive the basic algorithm and study its convergence properties within the framework of infinite dimensional pseudoconvex minimization. We also introduce a partial descent type auxiliary problem method which partially linearizes the objective functional and includes the auxiliary term only for a subset of variables. Numerous examples of this very general scheme are provided.