A short note on minx in Rn(||Ax-b||2 / 1+||x||2)

The goal of this short note is to provide an easy approach for solving a specific case of a fractional nonconvex minimization problem, which appears in the total least squares problem. We show that when the coefficient matrix is rank deficient, using convex optimization problems we can provide an optimal solution for the given nonconvex fractional minimization problem.