Modelling Some Robust Design Problems via Conic Optimization

Abstract

In this paper, we deal with modelling robust design problems via conic optimization. A robust design problem deals with finding a robust optimal solution of an uncertain design problem. The uncertain data is assumed to belong to a so-called uncertainty set $\mathcal{U}$. Uncertainty means that the data is not known exactly at the time when the solution has to be determined. In order to find a robust optimal solution, we use the robust optimization (RO) methodology of Ben-Tal and Nemirovskii. We demonstrate this on the robust shortest path problem (RSPP), the robust maximum flow problem (RMFP) and the robust resistance network topology design (RNTD) problem.