In the context of structured nonconvex optimization, we estimate the increase in minimum value for a decision that is robust to parameter perturbations as compared to the value of a nominal problem. The estimates rely on detailed expressions for subgradients and local Lipschitz moduli of min-value functions in nonconvex robust optimization and require only the solution of the nominal problem. The theoretical results are illustrated by examples from military operations research involving mixed-integer optimization models. Across 54 cases examined, the median error in estimating the increase in minimum value is 12%. Therefore, the derived expressions for subgradients and local Lipschitz moduli may accurately inform analysts about the possibility of obtaining cost-effective, parameter-robust decisions in nonconvex optimization.
翻译:在结构化非电流优化背景下,我们估计了与名义问题相比,对参数扰动具有强力作用的决定的最小值增长幅度。该估算值依赖于非电流稳健优化中小价值函数的亚梯度和本地Lipschitz模量的详细表达方式,仅需要解决名义问题。从涉及混合内位优化模型的军事行动研究中得出的实例中可以说明理论结果。在所审查的54个案例中,估算最小值增长的中值误差为12%。因此,亚梯度和本地Lipschitzmoduli的衍生表达方式可以准确地使分析家了解在非电流优化中获得成本效益高的参数-机器人决定的可能性。