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

本奖项的目标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，并使用极大值准则来解决函数歧义。对于许多数据驱动的决策问题，通过模型拟合从数据中得到指定问题的函数。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。将分析不同类型的函数鲁棒模型，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一类新的优化建模技术和算法的发展，以解决这些模型。在数据不确定的情况下，与传统的已知方法相比，该模型得到的解具有更强的鲁棒性和效率。允许函数形式的歧义的一般方法框架将为基于优化的决策制定领域提供重要的概念进步。这些问题的应用范围从管理、智能控制和工程设计的主题。将进行实验来验证算法，并比较由新建模技术生成的解决方案的特性。

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.