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.
