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Dual Dynamic Programming with cut selection: convergence proof and numerical experiments

Vincent Guigues(vincent.guigues***at***gmail.com)

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.

Keywords: Dynamic Programming ; Nonlinear programming; Decomposition algorithms; Dual Dynamic Programming; Pruning methods

Category 1: Convex and Nonsmooth Optimization

Category 2: Other Topics (Dynamic Programming )

Citation: V. Guigues, Dual Dynamic Programing with cut selection: Convergence proof and numerical experiments, European Journal of Operational Research, 258 (1): 47-57, 2017.

Download: [PDF]

Entry Submitted: 05/24/2017
Entry Accepted: 05/24/2017
Entry Last Modified: 05/24/2017

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