A non-linear conjugate gradient in dual space for L-norm regularized non-linear least squares with application in data assimilation

Antoine Bernigaud, Serge Gratton, Ehouarn Simon

Abstract: Wanting to minimize a non-linear least squares function penalized with an \(L_p\)-norm, with \(p\in (1,2)\), stemming from a 4DVar formulation of a data assimilation problem, we propose a modification of the non-linear conjugate gradient by making the iterations and the step search in the topological dual space of \(L_p\). We prove the convergence of this new algorithm and look at its performance on a data assimilation setup based on the shallow-water equations where the use of such an \(L_p\)-norm regularization is justified.