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，指定问题的函数是通过模型拟合从数据中获得的。 该模型拟合是基于函数的假定形式完成的。 随后通过优化拟合函数来做出决策。 在建模框架中，使用函数的属性和非参数模型拟合来指定函数集。 这类问题称为函数鲁棒优化问题。 本文将对不同类型的函数鲁棒模型进行分析，并提出求解这些模型的算法，如果成功，将为此类模型的优化建模技术和算法的发展提供新的思路。 从这样的模型得到的解决方案，预计将更强大和有效的数据不确定性相比，从经典的已知方法。 一个通用的方法框架，允许模糊的功能形式将提出一个显着的概念性的进步，以优化为基础的决策领域。 这些问题的应用范围从管理，智能控制和工程设计的主题。 实验将进行验证的算法，并比较新的建模技术产生的解决方案的属性。

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.