In this study, calibration maintenance confronts the problem of updating a model developed in the primary condition to accurately predict the calibrated analyte in samples measured in new secondary conditions. Calibration transfer refers to updating a model based on a primary instrument to predict samples measured on new secondary instruments. A 2-norm variant of Tikhonov regularization (TR) has been used with spectroscopic data to perform calibration maintenance and transfer where just a few samples measured in the secondary condition/instrument are augmented to the primary calibration data to update the primary model. To achieve improved predictions, in this paper we report on 1-norm penalties to create two novel variants of TR for model updating. To solve the multiple penalty minimization numerical problems involved with the new TR variants, data transformation processes are applied, allowing a least absolute shrinkage and selection operator type algorithm to be implemented. Near-infrared spectra measured under two different temperatures represent the calibration maintenance application, and near-infrared spectra measured on two instruments denote the calibration transfer situation. Compared to TR in the recently developed 2-norm penalty mode, validation sample prediction errors are reduced when the 1-norm TR variant that selects wavelengths is used.