This method will balance functions of the covariates within some tolerance, \(\delta\). For these functions \(B\), we will desire
$$\frac{\sum_{i: Z_i = 0} w_i B(x_i) - \sum_{j: Z_j = 1} B(x_j)/n_1}{\sigma} \leq \delta$$, where in this case we are targeting balance with the treatment group for the ATT. \(\sigma\) is the pooled standard deviation prior to balancing.