title: Lagrange-Newton Methods for Parameter Identification using Total Variation Regularization 

abstract:
The aim of this paper is to discuss Lagrange-Newton type method
for recovering sharp discontinuities for the ill-posed parameter
identification problems by using total variation (TV)
regularization. By approximating TV, we also discuss some variants
of the original Lagrange-Newton algorithm. Numerical experiments
indicate that the combination of these techniques enables us to
successfully recover discontinuous coefficients under reasonable
observation errors.