Optimization problems often involve unknown parameters; a commonly applied approach to circumvent this issue is to use observations of these parameters and predict them before optimizing. This "Predict, then Optimize" framework optimizes prediction error, not necessarily yielding the best decisions under parameter uncertainty. As an alternative, Elmachtoub and Grigas (2021) proposed the "Smart Predict, then Optimize" framework to generate prediction models minimizing decision error, instead. Here, a prediction model is designed by minimizing a "regret" function, capturing the error of making a sub-optimal decision due to an inaccurate prediction. The resulting problem can be formulated as a pessimistic bilevel optimization problem - inherently non-convex; Elmachtoub and Grigas thus propose a convex surrogate to obtain tractability. In this talk, we focus on solution methods for the exact non-convex pessimistic bilevel optimization problem. We reformulate the problem as a quadratically-constrained problem and show an extensive computational study in shortest-path instances comparing various solution methods, both existing and new.