This contribution is an extension of the work initiated in [1], presenting a strategy for the calibration of the local volatility. Due to Morozov's discrepancy principle [6], the Tikhonov regularization problem introduced in [7] is understood as an inequality-constrained minimization problem. An Uzawa procedure is proposed to replace this latter by a sequence of unconstrained problems dealt with in the modified Thikonov regularization procedure in [1]. Numerical tests confirm the consistency of the approach and the significant speed-up of the process of local volatility determination.