Semidefinite and Conic Programming for Robust wireless OFDMA networks

In this paper, we study three robust optimization approaches [Adasme Pablo, Abdel Lisser and Ismael Soto, Robust Semidefinite Relaxations for a New Quadratic OFDMA Resource Allocation Approach, Working Paper Number 1522, LRI, University of Paris Sud, France]. The first one is based on the worst case scenario approach from Kouvelis and Yu [Kouvelis, and G. Yu, Robust discrete optimization and its applications, Kluwer Academic Publishers, 1997]. The second, corresponds to a scaled simplex polyhedral approach due to Bertsimas and Sim [Bertsimas Dimitris, and Melvyn Sim, The Price of Robustness, Operations Research, 52 (2004)] whilst the third, correspond to an ellipsoidal uncertainty approach proposed by Ben Tal and Nemirovski [Ben-Tal Aharon, and Arkadi Nemirovski, Robust solutions of Linear Programming problems contaminated with uncertain data, Mathematical Programming, Springer Berlin-Heidelberg, 88 (2000), 411–424]. 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.