LAUSR

We study the problem of minimizing the ratio of quadratic functions with a quadratic constraint (QCRQ), which is a generation of the trust-region subproblem and covers the regularized total least square problem as a special case. In this paper, we carefully employ the bisection search method to solve the scaled Lagrangian dual of (QCRQ) as strong duality holds for the primal and dual problems. We show that our algorithm can globally solve the nonconvex optimization (QCRQ) in linear time. Numerical experiments demonstrate the computational efficiency over other semidefinite programming solvers.