Solving the complex quadratic double-ratio minimax optimization under a quadratic constraint

Complex quadratic double-ratio minimax optimization (CQRMO) problem under a quadratic constraint has the potential to solve the total least squares problem. In order to solve it, a variant of S-Lemma is proposed and found to be interesting because it leads to a generalized linear conic fractional problem. Then, we achieve the global optimum of CQRMO problem with a quadratic constraint by using two algorithms for the generalized linear conic fractional problem. The efficiency of the proposed algorithms is evaluated by several numerical examples.