Inverse Mixed Integer Optimization: Polyhedral Insights and Trust Region Methods

Inverse optimization—determining parameters of an optimization problem that render a given solution optimal—has received increasing attention in recent years. Although significant inverse literature exists for convex problems, there have been few advances discrete despite the ubiquity applications fundamentally rely on decision making. In this paper, we present new set theoretical insights and algorithms general class mixed integer linear problems. Specifically, characterization optimality conditions is established leveraged to design cutting plane algorithms. Through extensive computational experiments, show our methods provide substantial improvements over existing solving largest most difficult instances date.