Inexact Kleinman-Newton-ADI Method with Line Search to Solve Large-Scale Algebraic Riccati Equations

This poster shows recent improvements of the inexact Kleinman-Newton method for solving algebraic Riccati equations by incorporating a line search and by systematically integrating the low-rank structure resulting from ADI methods for the approximate solution of the Lyapunov equation that needs to be solved to compute the Kleinman-Newton step. A convergence result is pointed out that tailors the convergence proof for general inexact Newton methods to the structure of Riccati equations and avoids positive semi-definiteness assumptions on the difference between certain matrices and the Lyapunov equation residual, which in general do not hold for low-rank approaches. On a test example, the improved inexact Kleinman-Newton method demonstrates its advantages.