The augmented Lagrangian method based on the APG strategy for an inverse damped gyroscopic eigenvalue problem

In this paper, we propose an augmented Lagrangian method based on the accelerated proximal gradient (APG) strategy for an inverse damped gyroscopic eigenvalue problem (IDGEP), which is a special case of the classical inverse quadratic eigenvalue problem. Under mild conditions, we show that the whole sequence of iterations generated by the proposed algorithm converges to the unique solution of the IDGEP. In view of the iteration-complexity, the proposed algorithm requires at most outer iterations and at most APG calls to obtain an -feasible and -optimal solution of the IDGEP. Numerical results indicate that the proposed algorithm can solve the test problems efficiently.