Convex approximations for mixed-integer recourse models

Two-stage mixed-integer recourse models are a class of problems dealing with decision making under uncertainty. They have a wide range of applications in e.g., finance, energy, logistics and healthcare. However, in general these problems are extremely difficult to solve.

In this talk, we discuss convex approximations of these two-stage mixed-integer recourse models. The rationale of using these approximations is that they can be solved much more efficiently using techniques from convex optimization. Moreover, if the approximations are close they will yield good or (near-)optimal first-stage solutions. To guarantee the performance of these approximating first-stage solutions we derive error bounds on the convex approximations that depend on the total variations of the probability density functions of the random variables in the model. We will use an example in healthcare to illustrate the convex approximations and their error bounds.

In the final part of the talk, we discuss initial results for combining convex approximations with other solution approaches for solving mixed-integer recourse models. In particular, we propose an inexact cutting plane technique.

Registration to Remy Spliet, spliet@ese.eur.nl is required for availability of lunch.