Duality in Two-Stage Adaptive Linear Optimization: Faster Computation and Stronger Bounds
研究了两阶段自适应线性优化模型的对偶性，发现对偶模型与原模型结构相同但维度不同，且对偶仿射策略可直接得到原问题最优解，计算速度比原模型快一个数量级，并能提供更强的下界。
In this paper we derive and exploit duality in general two-stage adaptive linear optimization models. The equivalent dualized formulation we derive is again a two-stage adaptive linear optimization model. Therefore, all existing solution approaches for two-stage adaptive models can be used to solve or approximate the dual formulation. The new dualized model differs from the primal formulation in its dimension and uses a different description of the uncertainty set. We show that the optimal primal affine policy can be directly obtained from the optimal affine policy in the dual formulation. We provide empirical evidence that the dualized model in the context of two-stage lot-sizing on a network and two-stage facility location problems solves an order of magnitude faster than the primal formulation with affine policies. We also provide an explanation and associated empirical evidence that offer insight on which characteristics of the dualized formulation make computations faster. Furthermore, the affine policy of the dual formulations can be used to provide stronger lower bounds on the optimality of affine policies.