Dual Dynamic Programming with cut selection: convergence proof and numerical experiments
Optimization and Control
2017-05-26 v1
Abstract
We consider convex optimization problems formulated using dynamic programming equations. Such problems can be solved using the Dual Dynamic Programming algorithm combined with the Level 1 cut selection strategy or the Territory algorithm to select the most relevant Benders cuts. We propose a limited memory variant of Level 1 and show the convergence of DDP combined with the Territory algorithm, Level 1 or its variant for nonlinear optimization problems. In the special case of linear programs, we show convergence in a finite number of iterations. Numerical simulations illustrate the interest of our variant and show that it can be much quicker than a simplex algorithm on some large instances of portfolio selection and inventory problems.
Cite
@article{arxiv.1705.08941,
title = {Dual Dynamic Programming with cut selection: convergence proof and numerical experiments},
author = {Vincent Guigues},
journal= {arXiv preprint arXiv:1705.08941},
year = {2017}
}