The concept of distance in global optimization applied to non-linear inverse problems

A common approach to solve an inverse problem, i.e. to single out the model parameters that explain the observed phenomena, is to iteratively minimize a residual function, which expresses the difference between the observations (measured data) and the forward response of the estimated model (recalculated data). The convergence properties of the solver can be difficult to control and to analyse, especially when dealing with global optimizers applied to non-linear inverse problems. In this paper, we plot the residual vs. a single scalar, the Euclidian distance in the variable space. We show how this can be used to avoid misleading solutions given by the local minima. The performance of this approach is investigated in three examples with increasing complexity (in terms of dimensions). Moreover, we propose to exploit the distance indicator in a new hybrid inversion strategy that combines a simulated annealing algorithm and a local approach and that reduces the computational cost of the optimization. © 2013 © 2013 Taylor & Francis.