A generalized conditional gradient method for nonlinear operator equations with sparsity constraints

The intention of this paper is to show the applicability of a generalized conditional gradient method for the minimization of Tikhonov-type functionals, which occur in the regularization of nonlinear inverse problems with sparsity constraints. We consider functionals of Tikhonov type where the usual quadratic penalty term is replaced by the pth power of a weighted l(p)-norm. First of all, we analyze the convergence properties of a generalized gradient algorithm. Further, we show that the considered minimization method coincides under certain conditions with a surrogate method. Numerical results are then illustrated by means of the nonlinear single photon emission computed tomography problem.