Primal and dual decision rules for multi-stage robust optimization
1 : Institut de Recherche Mathématique de Rennes
Agrocampus Ouest, Universite de Rennes 1, Université de Rennes 2, École normale supérieure - Rennes, Centre National de la Recherche Scientifique : UMR6625, Institut National des Sciences Appliquées - Rennes
2 : UNIVERSITY OF TORONTO
In this work, we adapt the recent decision rules introduced in the stochastic programming literature to multi-stage robust optimization both from the primal and the dual perspective. From the primal perspective, we propose two-stage decision rules that restrict the functional forms of state variables only. From the dual perspective, we first write a Lagrangian dual based on the relaxation of non-anticipativity constraints. We then apply decision rules to the Lagrangian multipliers. The resulting problems are challenging and require advanced techniques in their solution. Our methodology is illustrated with preliminary results on production planning and transportation problems.