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

We compare the performance of several robust large-scale minimization algorithms applied for the minimization of the cost functional in the solution of ill-posed inverse problems related to parameter estimation applied to the parabolized Navier-Stokes equations. The methods compared consist of the conjugate gradient method (CG), Quasi-Newton (BFGS), the limited memory Quasi-Newton (L-BFGS) [1], Hessian Free Newton method [2,3] and a new hybrid algorithm proposed by Morales and Nocedal [4]. The hybrid method emerged as the best performer for an adequate choice of parameters controlling the number of L-BFGS and Hessian free iterations to be interlaced.