Interior Point Solving for LP-based prediction+optimisation

Solving optimization problem is the key to decision making in many real-life analytics applications. However, the coefficients of the optimization problems are often uncertain and dependent on external factors, such as future demand or energy- or stock prices. Machine learning (ML) models, especially neural networks, are increasingly being used to estimate these coefficients in a data-driven way. Hence, end-to-end predict-and-optimize approaches, which consider how effective the predicted values are to solve the optimization problem, have received increasing attention. In case of integer linear programming problems, a popular approach to overcome their non-differentiabilty is to add a quadratic penalty term to the continuous relaxation, such that results from differentiating over quadratic programs can be used.