Collaborative Research: Analysis and Solution Methods for Function Robust Optimization Models

该奖项的目的是研究一类新的优化模型，其中一般形状约束指定函数形式，并使用最大最小准则来解决函数模糊性。对于许多数据驱动的决策问题，描述问题的函数都是通过模型拟合从数据中得到的。该模型拟合是基于函数的假定形式进行的。随后，通过优化拟合函数来做出决定。在建模框架中，使用函数和非参数模型拟合的属性来指定函数集。这类问题称为函数稳健优化问题。将分析不同类型的函数稳健模型，并开发求解这些模型的算法。如果成功，这项研究的结果将导致开发一类新的优化建模技术和算法来求解此类模型。与经典的已知方法相比，在数据不确定的情况下，由这类模型得到的解有望更加稳健和有效。允许函数形式模糊性的通用方法学框架将为基于优化的决策领域带来重大的概念上的进步。这些问题的应用范围广泛，从管理、智能控制和工程设计的主题。将进行实验以验证算法，并比较由新的建模技术生成的解的性质。

The objective of this award is to study a new class of optimization models where general shape constraints specify the function form, and a maximin criterion is used to resolve the function ambiguity. For many data driven decision problems the functions specifying the problem are obtained from the data through model fitting. This model fitting is done based on a presumed form of the function. The decisions are subsequently made by optimizing the fitted functions. In the modeling framework the function set is specified using properties of the function and non-parametric model fitting. Such problems are called function robust optimization problems. Different types of function robust models will be analyzed and algorithms will be developed for solving these models.If successful, the results of this research will lead to the development of a new class of optimization modeling techniques and algorithms for solving such models. The solutions obtained from such models are expected to be more robust and efficient under data uncertainty when compared to those obtained from the classical known approaches. A general methodological framework that allows ambiguity in the function form will present a significant conceptual advancement to the field of optimization based decision making. Applications of such problems range from topics in management, intelligent control, and engineering design. Experiments will be performed to validate the algorithms, and to compare the properties of the solutions generated from the new modeling technique.