Robust convex optimization: a new perspective that unifies and extends
Journal
Mathematical Programming
Subject
Management Science and Operations
Publishing details
Authors / Editors
Bertsimas D;den Hertog D;Pauphilet J;Zhen J
Biographies
Publication Year
2023
Abstract
Robust convex constraints are difficult to handle, since finding the worst-case scenario is equivalent to maximizing a convex function. In this paper, we propose a new approach to deal with such constraints that unifies most approaches known in the literature and extends them in a significant way. The extension is either obtaining better solutions than the ones proposed in the literature, or obtaining solutions for classes of problems unaddressed by previous approaches. Our solution is based on an extension of the Reformulation-Linearization-Technique, and can be applied to general convex inequalities and general convex uncertainty sets. It generates a sequence of conservative approximations which can be used to obtain both upper- and lower- bounds for the optimal objective value. We illustrate the numerical benefit of our approach on a robust control and robust geometric optimization example.
Available on ECCH
No
