Semidefinite relaxation for the total least squares problem with Tikhonov-like regularization

We study the total least squares (TLS) with a parametric Tikhonov-like regularization. We relax it to a semidefinite programming (SDP) problem and establish a sufficient condition to guarantee the tightness of the SDP relaxation. This special-structured SDP relaxation is further reformulated as a univariate maximization and then solved by the bisection method. Numerical results demonstrate that the bisection algorithm highly outperforms the SDP solver SeDuMi. Finally, based on the newly proposed (SDP), we propose a new SDP relaxation for (TLS) with canonical Tikhonov regularization and then employ an outer approximation scheme to solve this SDP relaxation.