| Inverse optimization has recently received a growing amount of attention as a data-driven approach to determining parameter values for an optimization problem. In this thesis, we study new inverse optimization methodologies that generalize the traditional method of solving inverse optimization problems and accommodate data that makes the standard method ill-posed. We apply the proposed methodologies to prostate cancer therapy data and provide novel insights for radiation therapy treatment planning.;In the first part of the thesis, we briefly review recent theoretical development of inverse optimization and discuss how this thesis contributes to the literature. In the second part of the thesis, we describe a motivational example in radiation therapy treatment planning and illustrate the problem settings and clinical data.;In the third part of the thesis, we develop generalized inverse linear optimization models. We characterize the relationship between the generalized models and the standard model in the literature. By building on the models in general inverse multiobjective optimization problems, we establish a new connection between inverse optimization and existing multiobjective optimization techniques. We show how our methods can be used for determining objective function weights for radiation therapy treatment planning.;Next, we present a clinical application of the results from the previous part of the thesis, by proposing a statistical model that relates the objective function weights to a patient's anatomical characteristics. Using the statistical relationship, we propose a prediction model that infers objective function weights from patient anatomy and provide a proof of concept of automated, knowledge-based weight determination for radiation therapy treatment planning.;Finally, we extend the theory of the second part of the thesis by developing generalized inverse convex optimization models. In the multiobjective optimization framework, we propose inverse convex optimization models that preserve the preference ordering among different objectives that is encoded by given data, and compare our models to existing inverse optimization models using prostate cancer therapy data. We present a unifying framework that encompasses many of the inverse optimization models in the literature. |
