Partially penalized calibration is a method to obtain weights that allow exact estimation of the total of several auxiliary variables and the approximate estimation of the total of other variables. It was suggested by Bardsley and Chambers (1984), in a modelbased setting, and by Guggemos and Tillé (2010), in a calibration setting. They proposed two different optimization problems to obtain such weights. In this paper, we show that the two optimization problems lead to the same solution.