Technical Note—Dual Approach for Two-Stage Robust Nonlinear Optimization
研究了两阶段可调鲁棒最小化问题，其中目标或约束对可调变量是凸的。通过将原问题转化为等价的可调鲁棒线性问题，可利用现有线性方法求解，并恢复线性决策规则和最优值界。
In “Dual Approach for Two-Stage Robust Nonlinear Optimization,” de Ruiter, Zhen, and den Hertog study adjustable robust minimization problems where the objective or constraints depend in a convex way on the adjustable variables. They reformulate the original adjustable robust nonlinear problem with a polyhedral uncertainty set into an equivalent adjustable robust linear problem, for which all existing approaches for adjustable robust linear problems can be used. The reformulation is obtained by first dualizing over the adjustable variables and then over the uncertain parameters. The polyhedral structure of the uncertainty set then appears in the linear constraints of the dualized problem, and the nonlinear functions of the adjustable variables in the original problem appear in the uncertainty set of the dualized problem. The authors show how to recover linear decision rules to the original primal problem and how to generate bounds on its optimal objective value.