In this paper we show that two-stage adjustable robust linear programs with affinely adjustable data in the face of box data uncertainties under separable quadratic decision rules admit exact semi-definite program (SDP) reformulations in the sense that they share the same optimal values and admit a one-to-one correspondence between the optimal solutions. This result allows adjustable robust solutions of these robust linear programs to be found by simply numerically solving their SDP reformulations. We achieve this result by first proving a special sum-of-squares representation of non-negativity of a separable non-convex quadratic function over box constraints. Our reformulation scheme is illustrated via numerical experiments by applying it to an inventory-production management problem with the demand uncertainty. They demonstrate that our separable quadratic decision rule method to two-stage decision-making performs better than the single-stage approach and is capable of solving the inventory production problem with a greater degree of uncertainty in the demand.

在本文中，我们展示了在可分离二次决策规则下面对盒数据不确定性的具有仿射可调数据的两阶段可调鲁棒线性规划允许精确半定规划 (SDP) 重构，因为它们共享相同的最优值和承认最优解之间的一一对应关系。该结果允许通过简单地数值求解它们的 SDP 重构来找到这些鲁棒线性程序的可调鲁棒解。我们通过首先证明可分离非凸二次函数在框约束上的非负性的特殊平方和表示来实现这一结果。通过将其应用于具有需求不确定性的库存生产管理问题，我们通过数值实验说明了我们的重新配方方案。