We develop a new inverse optimization framework to infer the constraint parameters of a linear (forward) optimization based on multiple observations of the system. The goal is to find a feasible region for the forward problem such that all given observations become feasible and the preferred observations become optimal. We explore the theoretical properties of the model and develop computationally efficient equivalent models. We consider an array of functions to capture various desirable properties of the inferred feasible region. We apply our method to radiation therapy treatment planning—a complex optimization problem in itself—to understand the clinical guidelines that in practice are used by oncologists. These guidelines (constraints) will standardize the practice, increase planning efficiency and automation, and make high-quality personalized treatment plans for cancer patients possible.