Solving a type of the Tikhonov regularization of the total least squares problem by a new version of S-Lemma

Time: 10:00 to  11:30 Ngày 16/01/2019

Venue/Location: C2-714, VIASM

Speaker: Prof. Ruey-Lin Sheu


Total Least Squares (TLS) is a method for fitting an overdetermined linear system Ax=b while assuming that both A and b are contaminated with noise. However, the TLS does not always have a solution; or even if it does, might frequently be ill-posed. The Tikhonov regularization which associated the TLS with a quadratic penalty is thus a technique for stabilizing the solution. Beck and Ben-Tal in 2006 (Siam J. Optim.) were the first to study the problem, but the formula (54) in their paper was unfortunately wrong. As such, all subsequent analysis and related computation after (54), including Algorithm TRTLSI itself, should be modified accordingly. In this talk, we provide another way to solve the problem via a new version of S-Lemma with two equalities. The result is neat, and can be generalized to optimize a special type of polynomial of degree 4. The result also covers our early papers on minimizing the double well potential problems.