Column generation algorithms for nonlinear optimization, I: Convergence analysis
- Ricardo Garćıa, Angel Maŕın, Michael Patriksson
The descent auxiliary problem method allows one to nd 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 innnite 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 of subset of variables. Numerous examples of this very general scheme are provided.