论文标题
连接不确定性下的优化
Optimization under Connected Uncertainty
论文作者
论文摘要
强大的优化方法已在不确定性下的各种决策应用中显示出实际的优势。最近，它们的功效已扩展到多周期设置。当前的方法通过预算总体不确定性来模拟独立于过去或隐式方式的不确定性。但是，在许多应用中，过去的实现直接影响未来的不确定性。对于此类问题，我们开发了一个建模框架，该框架通过连接的不确定性集明确地合并了这种依赖性，每个时期的参数取决于先前的不确定性实现。为了找到最佳的这里和现在的解决方案，我们对流行的集合结构进行了鲁棒和分布的强大约束，并在广泛适用的背包和投资组合优化问题上以数字形式证明了这种建模框架。
Robust optimization methods have shown practical advantages in a wide range of decision-making applications under uncertainty. Recently, their efficacy has been extended to multi-period settings. Current approaches model uncertainty either independent of the past or in an implicit fashion by budgeting the aggregate uncertainty. In many applications, however, past realizations directly influence future uncertainties. For this class of problems, we develop a modeling framework that explicitly incorporates this dependence via connected uncertainty sets, whose parameters at each period depend on previous uncertainty realizations. To find optimal here-and-now solutions, we reformulate robust and distributionally robust constraints for popular set structures and demonstrate this modeling framework numerically on broadly applicable knapsack and portfolio-optimization problems.
