标题： 线性、嵌套和二次有序度量：计算及其在优化问题中的应用 显示英文标题

标题： Linear, nested, and quadratic ordered measures: Computation and incorporation into optimization problems

摘要： 在本文中，我们提出一个统一的数学优化框架，以计算大多数运筹学和数据科学情境中使用的广泛度量。 目标是将这些度量嵌入到通用优化模型中，从而实现它们的高效计算。 我们评估了这种方法的实用性，并将其应用于三种不同的度量族，即线性、嵌套和二次有序度量。 报告了计算结果，展示了与数值软件包中的标准实现相比，我们方法的效率和准确性。 最后，我们通过在三个著名的线性和组合优化问题上计算相对于不同度量的最佳解来说明这种方法：线性规划中的情景分析，旅行商问题和加权多覆盖集问题。 显示英文摘要

摘要： In this paper we address a unified mathematical optimization framework to compute a wide range of measures used in most operations research and data science contexts. The goal is to embed such metrics within general optimization models allowing their efficient computation. We assess the usefulness of this approach applying it to three different families of measures, namely linear, nested, and quadratic ordered measures. Computational results are reported showing the efficiency and accuracy of our methods as compared with standard implementations in numerical software packages. Finally, we illustrate this methodology by computing a number of optimal solutions with respect to different metrics on three well-known linear and combinatorial optimization problems: scenario analysis in linear programming, the traveling salesman and the weighted multicover set problem.