What can copositive programming do for MSRO problems?

We have completed a manuscript to address the challenging decision rule approximations for generic multi-stage robust optimization problems. We use the very powerful copositive programming to model the approximation problems, based

on which we propose high-quality solution schemes. We have posted the manuscript on Optimization Online.

We study decision rule approximations for generic multi-stage robust linear optimization prob- lems. We consider linear decision rules for the case when the objective coefficients, the recourse matrices, and the right-hand sides are uncertain, and consider quadratic decision rules for the case when only the right-hand sides are uncertain. The resulting optimization problems are NP-hard but amenable to copositive programming reformulations that give rise to tight con- servative approximations. We further enhance these approximations through new piecewise decision rule schemes. Finally, we prove that our proposed approximations are tighter than the state-of-the-art schemes and demonstrate their superiority through numerical experiments.

For details, we refer the reader to the post on Optimization Online.