The past decade has seen an intense research focus on developing models and studying solution approaches for obtaining ``robust solutions" of optimization problems that are insensitive to parameter uncertainty. This research assumes that the parameters specifying the functions in the optimization problem are uncertain. We propose to study optimization models where shape constraints specify the function form and a maximin criterion is used to resolve function ambiguity. We call such problems function robust optimization problems. Specifically, we propose to study a maximin decision making framework that uses a set of model functions instead of an ambiguity set for the parameter data. The function set is specified using model properties of the function learned from partial known information (e.g., increasing, convex, etc.), and possibly non-parametric model fitting. Additional boundary and auxiliary requirements defining the set of functions may be present. For example, bounds on a multivariate function and its first and second derivative specify a region of ambiguity for the true function; and auxiliary conditions may be used to link the construction of the function set with classical model fitting techniques.
|Effective start/end date||9/1/14 → 8/31/19|
- National Science Foundation (CMMI-1361942)