9/24/20 | 4:15pm | Online only
Dick den Hertog
University of Amsterdam
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 all 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 the Reformulation-Perspectification-Technique (RPT), and can be applied to general convex inequalities and general convex uncertainty sets. It generates a sequence of conservative approximations and 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.
Bio: Dick den Hertog is professor of Operations Research at University of Amsterdam. His research interests cover various fields in prescriptive analytics, in particular linear and nonlinear optimization. In recent years his main focus has been on robust optimization. He is also active in applying the theory in real-life applications. In particular, he is interested in applications that contribute to a better society. For many years he has been involved in research for optimal flood protection, which was awarded by the INFORMS Franz Edelman Award in 2013. Currently, he is doing research to develop better optimization models and techniques for cancer treatment, and he is involved in research to optimize the food supply chain for Zero Hunger. He is chairman of the Dutch Network on the Mathematics of Operations Research, and associate editor of Operations Research, and INFORMS Journal on Optimization.