Robust binary least squares: Relaxations and algorithms

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 coef cient 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 semide nite relaxation (SDR)-based approximations. However, the relaxation step is not obvious, and requires a certain problem reformulation to be ef cient. 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.

• Type: Journal
• Year: 2011
• Where: ICASSP
• Authors: Efthymios Tsakonas, Joakim Jalden, Björn E. Ottersten
• Keywords: Binary Ls Problems, Certain Problem Reformulation, ICASSP 2011, Robust Optimization Problem, Signal Processing