In this talk, we discuss three robust optimization approaches. The first one is based on the worst case scenario approach from Kouvelis and Yu (1997), the second one corresponds to a scaled simplex polyhedral approach due to Bertsimas and Sim (2004) whilst the last one corresponds to an ellipsoidal uncertainty approach proposed by Ben Tal and Nemirovski (2000). The study of the different approaches is made on the basis of a binary quadratic constrained program (BQCP). We derive two semidefinite programming (SDP) relaxations for the first two approaches whilst we use a second order conic program for the last one. Numerical results are given for a resource allocation of OFDMA wireless networks. We show that non-linear approches, namely Ben Tal and Nemiroski's method is competitive with Bertsimas linear one.
Groupe d’études et de recherche en analyse des décisions