Comparison of advanced large-scale minimization algorithms for the solution of inverse ill-posed problems

We compare the performance of several robust large-scale minimization algorithms for the unconstrained minimization of an ill-posed inverse problem. The parabolized Navier-Stokes equations model was used for adjoint parameter estimation. The methods compared consist of two versions of the nonlinear conjugate gradient method (CG), Quasi-Newton (BFGS), the limited memory Quasi-Newton (L-BFGS) [15], Truncated Newton method [19, 20] and a new hybrid algorithm proposed by Morales and Nocedal [16]. For all the methods employed and tested the gradient of the cost function is obtained via an adjoint method. A detailed description of the algorithmic form of minimization algorithms employed in the minimization comparison is provided. The hybrid method emerged as the best performer for an adequate choice of parameters controlling the number of L-BFGS and Truncated Newton iterations to be interlaced.