Ottersten, Björn[University of Luxembourg > Interdisciplinary Centre for Security, Reliability and Trust (SNT) > >]

2011

Acoustics, Speech and Signal Processing (ICASSP), 2011 IEEE International Conference on

IEEE

3780-3783

Yes

International

978-1-4577-0538-0

Proceedings IEEE International Conference on Acoustics,Speech and Signal Processing (ICASSP)

22-27 May 2011

Prague

Czech Republic

[en] Finding the least squares (LS) solution s to a system of linear equations Hs = y where H, y are given and s is a vector of binary variables, is a well known NP-hard problem. In this paper, we consider binary LS problems under the assumption that the coefficient matrix H is also unknown, and lies in a given uncertainty ellipsoid. We show that the corresponding worst-case robust optimization problem, although NP-hard, is still amenable to semidefinite relaxation (SDR)-based approximations. However, the relaxation step is not obvious, and requires a certain problem reformulation to be efficient. The proposed relaxation is motivated using Lagrangian duality and simulations suggest that it performs well, offering a robust alternative over the traditional SDR approaches for binary LS problems.