The main task of this work is solving an Optimal Transport (OT) problem applied to the color transfer field. Due to the various issues that can be encountered while solving it, we tackle the relaxation approach of the OT problem by relaxing one of its constraints. We solve it using the Frank-Wolfe algorithm and two of its variants: Block-Coordinate Frank-Wolfe, and Block- Coordinate Away Frank-Wolfe, which is supposed to give even better results. We employ different values of the relaxation parameter and/or the number of iterations in order to improve the baseline results and compare the outputs of the different values used. The assessment was done by analyzing the objective function and by observing the results of the color-transferred images in each case.