"Utility Preference Robust Optimization", talk by Dr Shaoyan Guo (Dalian University of Technology) Event

Event details

Utility preference robust optimization (PRO) models are recently proposed to deal with decision making problems where information on decision maker's utility preference is incomplete and has to be elicited through partial information such as questionnaires and pairwise comparisons, and the optimal decision is based on the worst case utility function elicited. In this paper, we examine an extension of the model to situations where the underlying utility functions are nonconcave, the ambiguity set of elicited utility functions is dependent on decision variables and the domain of the utility functions is unbounded. To solve the resulting maximin optimization problem, we propose a piecewise linear approximation (PLA) scheme for the ambiguity set. An immediate benefit of the PLA scheme is that it enables us to solve the inner utility minimization problem by solving a linear programming problem regardless of whether the elicited utility functions are concave or merely increasing or dependent on decision variables. To justify the PLA scheme, we derive an error bound for the approximated ambiguity set and the optimal value of the resulting maximin problem. The error bound provides an interval of the approximated optimal value.