论文标题
关于非凸优化的鲁棒性，并应用于国防计划
On Robustness in Nonconvex Optimization with Application to Defense Planning
论文作者
论文摘要
在结构化的非凸优化的背景下，我们估计与名义问题值相比，对参数扰动的决策的最小值增加。估计值依赖于在非凸功能中的Min-value功能的亚级别和局部Lipschitz模量的详细表达式，仅需要标称问题的解决方案。从涉及混合成员优化模型的军事行动研究的示例中说明了理论结果。在检查的54例病例中，估计最低值增加的中位误差为12％。因此，亚级别和局部Lipschitz模量的派生表达式可能会准确地告知分析师在非convex优化中获得具有成本效益的参数刺激决策的可能性。
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.
